diff --git a/jax/_src/pallas/core.py b/jax/_src/pallas/core.py
index 9143acbd0..4692e7791 100644
--- a/jax/_src/pallas/core.py
+++ b/jax/_src/pallas/core.py
@@ -296,10 +296,12 @@ def _preprocess_grid(grid: Grid | int | None) -> Grid:
 def _convert_block_spec_to_block_mapping(
     in_avals: Sequence[jax_core.ShapedArray],
     block_spec: BlockSpec,
+    path: tree_util.KeyPath,
     aval: jax_core.ShapedArray,
     in_tree: Any,
     grid: GridMappingGrid,
     mapped_dims: tuple[int, ...],
+    what: str,  # Used to localize error messages, e.g., {what}{path}
 ) -> BlockMapping | None:
   if block_spec is no_block_spec:
     return None
@@ -313,7 +315,13 @@ def _convert_block_spec_to_block_mapping(
       mapped if s is None else s for s in block_shape)
   flat_fun, _ = api_util.flatten_fun(lu.wrap_init(compute_index), in_tree)
   with tracing_grid_env(grid, mapped_dims):
-    jaxpr, _, consts, () = pe.trace_to_jaxpr_dynamic(flat_fun, in_avals)
+    jaxpr, out_avals, consts, () = pe.trace_to_jaxpr_dynamic(flat_fun, in_avals)
+    if len(out_avals) != len(block_shape):
+      raise ValueError(
+          f"Index map for {what}{tree_util.keystr(path)} must return "
+          f"{len(aval.shape)} values to match {block_shape=}. "
+          f"Currently returning {len(out_avals)} values."
+      )
   return BlockMapping(
       block_shape, jax_core.ClosedJaxpr(jaxpr, consts), block_spec.indexing_mode
   )
@@ -327,42 +335,51 @@ def _tile_ref(ref: state.AbstractRef, block_shape: tuple[int, ...] | None
   return ref.update(inner_aval=ref.inner_aval.update(shape=shape))
 
 
-def _check_static_ref_shape(ref: state.AbstractRef) -> state.AbstractRef:
-  shape = ref.shape
-  if not jax_core.is_constant_shape(shape):
-    # TODO(necula): thread the tree labels so that we can localize the error
-    raise ValueError("shape polymorphism for Pallas does not support "
-                     f"dynamically-shaped blocks. Found block_shape: {shape}")
-  return ref
-
-
-def _get_ref_avals(grid, in_avals, in_specs, out_avals, out_specs):
-  def _get_memory_space(spec):
+def _get_ref_avals(grid,
+                   in_avals: Sequence[jax_core.ShapedArray],
+                   in_specs: Sequence[BlockSpec],
+                   in_paths: Sequence[tree_util.KeyPath],
+                   out_avals: Sequence[jax_core.ShapedArray],
+                   out_specs: Sequence[BlockSpec],
+                   out_paths: Sequence[tree_util.KeyPath]):
+  def make_ref_aval(aval: jax_core.ShapedArray,
+                    spec: BlockSpec,
+                    path: tree_util.KeyPath,
+                    what: str) -> state.AbstractRef:
     if spec is no_block_spec:
-      return None
-    return spec.memory_space
+      memory_space = None
+      block_shape = None
+    else:
+      memory_space = spec.memory_space
+      block_shape = spec.block_shape
+
+    ref_aval = AbstractMemoryRef(aval, memory_space)
+    if block_shape is not None:
+      if len(ref_aval.shape) != len(block_shape):
+        raise ValueError(
+            f"Block shape for {what}{tree_util.keystr(path)} (= {block_shape}) "
+            f"must have the same number of dimensions as the array shape {ref_aval.shape}"
+        )
+      trimmed_block_shape = tuple(s for s in block_shape if s is not None)
+      ref_aval = ref_aval.update(
+          inner_aval=ref_aval.inner_aval.update(shape=trimmed_block_shape))
+
+    if not jax_core.is_constant_shape(ref_aval.shape):
+      raise ValueError(
+          "shape polymorphism for Pallas does not support "
+          "dynamically-shaped blocks. "
+          f"{what}{tree_util.keystr(path)} has block_shape: {ref_aval.shape}")
+    return ref_aval
+
   in_ref_avals = [
-      AbstractMemoryRef(aval, _get_memory_space(in_spec))
-      for aval, in_spec in zip(in_avals, in_specs)
+      make_ref_aval(aval, in_spec, in_path, "input")
+      for aval, in_spec, in_path in zip(in_avals, in_specs, in_paths)
   ]
   out_ref_avals = [
-      AbstractMemoryRef(aval, _get_memory_space(out_spec))
-      for aval, out_spec in zip(out_avals, out_specs)
+      make_ref_aval(aval, out_spec, out_path, "output")
+      for aval, out_spec, out_path in zip(out_avals, out_specs, out_paths)
   ]
-  if grid is None:
-    in_specs = [None] * len(in_avals)
-    out_specs = [None] * len(out_avals)
-  tiled_in_ref_avals = [
-      _check_static_ref_shape(aval if in_spec is no_block_spec
-                              else _tile_ref(aval, in_spec.block_shape))
-      for aval, in_spec in zip(in_ref_avals, in_specs)
-  ]
-  tiled_out_ref_avals = [
-      _check_static_ref_shape(aval if out_spec is no_block_spec
-                              else _tile_ref(aval, out_spec.block_shape))
-      for aval, out_spec in zip(out_ref_avals, out_specs)
-  ]
-  return in_specs, tiled_in_ref_avals, out_specs, tiled_out_ref_avals
+  return in_specs, in_ref_avals, out_specs, out_ref_avals
 
 class NoBlockSpec:
   pass
@@ -386,6 +403,8 @@ class GridSpec:
     # Be more lenient for in/out_specs
     if isinstance(in_specs, list):
       in_specs = tuple(in_specs)
+    elif in_specs is not no_block_spec and not isinstance(in_specs, Sequence):
+      raise ValueError(f"`in_specs` must be a tuple or a list. Found: {in_specs}")
     if isinstance(out_specs, list):
       out_specs = tuple(out_specs)
 
@@ -410,20 +429,20 @@ class GridSpec:
       flat_in_specs = self.in_specs
       if self.in_specs_tree != in_tree:
         raise ValueError(
-            "Pytree specs for arguments and `in_specs` must match: "
-            f"{in_tree} vs. {self.in_specs_tree}")
+            pytreedef_mismatch_err_msg("`in_specs`", self.in_specs_tree,
+                                       "inputs", in_tree))
     if self.out_specs is no_block_spec:
       flat_out_specs = [no_block_spec] * len(out_avals)
     else:
       flat_out_specs = self.out_specs
       if self.out_specs_tree != out_tree:
         raise ValueError(
-            "Pytree specs for `out_shape` and `out_specs` must match: "
-            f"{out_tree} vs. {self.out_specs_tree}")
+            pytreedef_mismatch_err_msg("`out_specs`", self.out_specs_tree,
+                                       "`out_shape`", out_tree))
     return flat_in_specs, flat_out_specs
 
   def get_grid_mapping(
-      self, in_avals, in_tree, out_avals, out_tree
+      self, in_avals, in_tree, in_paths, out_avals, out_tree, out_paths
   ) -> tuple[tuple[jax_core.AbstractValue, ...], GridMapping]:
     assert all(i is None or isinstance(i, int) for i in self.grid)
     grid_mapping_grid = tuple(
@@ -432,8 +451,8 @@ class GridSpec:
     flat_in_specs, flat_out_specs = self._get_in_out_specs(
         in_avals, in_tree, out_avals, out_tree)
     in_specs, in_ref_avals, out_specs, out_ref_avals = _get_ref_avals(
-        self.grid, in_avals, flat_in_specs, out_avals,
-        flat_out_specs)
+        self.grid, in_avals, flat_in_specs, in_paths,
+        out_avals, flat_out_specs, out_paths)
     grid_avals = [jax_core.ShapedArray((), jnp.dtype("int32"))] * len(self.grid)
     # Create args, kwargs pytree def
     grid_tree = tree_util.tree_structure((tuple(grid_avals), {}))
@@ -444,8 +463,10 @@ class GridSpec:
             in_tree=grid_tree,
             grid=grid_mapping_grid,
             mapped_dims=(),
+            what="input",
         ),
         in_specs,
+        in_paths,
         in_ref_avals,
     )
     out_block_mappings = map(
@@ -455,8 +476,10 @@ class GridSpec:
             in_tree=grid_tree,
             grid=grid_mapping_grid,
             mapped_dims=(),
+            what="output",
         ),
         out_specs,
+        out_paths,
         out_ref_avals,
     )
     grid_mapping = GridMapping(
@@ -480,3 +503,18 @@ class GridSpec:
     static_self = copy.copy(self)
     static_self.grid = static_grid  # type: ignore
     return static_self, dynamic_bounds
+
+def pytreedef_mismatch_err_msg(
+    what1: str, tree1: tree_util.PyTreeDef,
+    what2: str, tree2: tree_util.PyTreeDef) -> str:
+  errs = list(tree_util.equality_errors_pytreedef(tree1, tree2))
+  msg = []
+  msg.append(
+      f"Pytree for {what1} and {what2} do not match. "
+      f"There are {len(errs)} mismatches, including:")
+  for path, thing1, thing2, explanation in errs:
+    where = f"at {tree_util.keystr(path)}, " if path else ""
+    msg.append(
+        f"    * {where}{what1} is a {thing1} but"
+        f" {what2} is a {thing2}, so {explanation}")
+  return "\n".join(msg)
diff --git a/jax/_src/pallas/mosaic/core.py b/jax/_src/pallas/mosaic/core.py
index f4a794792..09979faf8 100644
--- a/jax/_src/pallas/mosaic/core.py
+++ b/jax/_src/pallas/mosaic/core.py
@@ -170,7 +170,7 @@ class PrefetchScalarGridSpec(pallas_core.GridSpec):
     self.scratch_shapes = tuple(scratch_shapes)
 
   def get_grid_mapping(
-      self, in_avals, in_tree, out_avals, out_tree
+      self, in_avals, in_tree, in_paths, out_avals, out_tree, out_paths
   ) -> tuple[tuple[jax_core.AbstractValue, ...], GridMapping]:
     assert all(i is None or isinstance(i, int) for i in self.grid)
     grid_mapping_grid = tuple(
@@ -189,8 +189,8 @@ class PrefetchScalarGridSpec(pallas_core.GridSpec):
         in_avals, in_avals_tree, out_avals, out_tree)
     in_specs, in_ref_avals, out_specs, out_ref_avals = (
         pallas_core._get_ref_avals(
-            self.grid, in_avals, flat_in_specs,
-            out_avals, flat_out_specs))
+            self.grid, in_avals, flat_in_specs, in_paths[num_flat_scalar_prefetch:],
+            out_avals, flat_out_specs, out_paths))
     scalar_ref_avals = [
         AbstractMemoryRef(jax_core.ShapedArray(aval.shape, aval.dtype),
                           TPUMemorySpace.SMEM)
@@ -207,8 +207,10 @@ class PrefetchScalarGridSpec(pallas_core.GridSpec):
             in_tree=index_map_in_tree,
             grid=grid_mapping_grid,
             mapped_dims=(),
+            what="input",
         ),
         in_specs,
+        in_paths[num_flat_scalar_prefetch:],
         in_ref_avals,
     )
     out_block_mappings = map(
@@ -218,8 +220,10 @@ class PrefetchScalarGridSpec(pallas_core.GridSpec):
             in_tree=index_map_in_tree,
             grid=grid_mapping_grid,
             mapped_dims=(),
+            what="output",
         ),
         out_specs,
+        out_paths,
         out_ref_avals,
     )
     grid_mapping = GridMapping(
diff --git a/jax/_src/pallas/mosaic/lowering.py b/jax/_src/pallas/mosaic/lowering.py
index f47657a7a..1e011ee50 100644
--- a/jax/_src/pallas/mosaic/lowering.py
+++ b/jax/_src/pallas/mosaic/lowering.py
@@ -22,10 +22,10 @@ import string
 from typing import Any
 
 import jax
-from jax import core as jax_core
 from jax import lax
 from jax import tree_util
 from jax._src import ad_util
+from jax._src import core as jax_core
 from jax._src import custom_derivatives
 from jax._src import debugging
 from jax._src import dtypes
@@ -204,6 +204,11 @@ def ir_constant(x, mlir_type=None):
 lowering_rules = {}
 skip_mlir_conversions = set()
 
+def _get_aval_physical_dtype_shape(aval):
+  dtype_physical_shape = jax_core.physical_aval(aval).shape[
+      len(aval.shape) :
+  ]
+  return dtype_physical_shape
 
 def _get_arg_type(
     aval,
@@ -427,6 +432,7 @@ def lower_jaxpr_to_module(
       mlir_func = lower_jaxpr_to_transform_func(
           ctx,
           bm.index_map_jaxpr.jaxpr,
+          aval,
           name=func_name,
           mosaic_grid_mapping=mosaic_grid_mapping,
       )
@@ -434,6 +440,9 @@ def lower_jaxpr_to_module(
       block_shape = [
           1 if b is pl_core.mapped else b for b in bm.block_shape
       ]
+      # If we have an extended dtype, we need to add the block shape for the
+      # remaining physical dtype.
+      block_shape += list(_get_aval_physical_dtype_shape(aval.inner_aval))
       window_shape = ir.DenseI64ArrayAttr.get(block_shape)
       block_params = dict(
           window_bounds=window_shape,
@@ -469,6 +478,7 @@ def lower_jaxpr_to_module(
 def lower_jaxpr_to_transform_func(
     ctx: ir.Context,
     jaxpr: jax_core.Jaxpr,
+    aval: jax_core.AbstractValue,
     *,
     name: str,
     mosaic_grid_mapping: MosaicGridMapping,
@@ -503,8 +513,16 @@ def lower_jaxpr_to_transform_func(
         mesh_context=mesh_context,
         traceback_caches=mlir.TracebackCaches(),
     )
-    return jaxpr_subcomp(lowering_context, jaxpr, *jaxpr_indices,
-                         *scalar_prefetch)
+    out = jaxpr_subcomp(lowering_context, jaxpr, *jaxpr_indices,
+                        *scalar_prefetch)
+    assert isinstance(aval, state.AbstractRef), aval
+    # If we have an extended dtype, we need to add 0s for the block indices
+    # for the remaining physical dtype.
+    out += [
+        ir_constant(0, mlir_type=_dtype_to_ir_type(jnp.dtype("int32")))
+    ] * len(_get_aval_physical_dtype_shape(aval.inner_aval))
+    return out
+
   body_func.__name__ = name
   body = func.FuncOp.from_py_func(*arg_types, name=name)(body_func)
   try:
diff --git a/jax/_src/pallas/pallas_call.py b/jax/_src/pallas/pallas_call.py
index 41b2d2e61..66678076e 100644
--- a/jax/_src/pallas/pallas_call.py
+++ b/jax/_src/pallas/pallas_call.py
@@ -23,7 +23,6 @@ from typing import Any
 import jax
 from jax import api_util
 from jax import lax
-from jax import tree_util
 from jax._src import ad_util
 from jax._src import checkify
 from jax._src import config
@@ -31,6 +30,7 @@ from jax._src import core as jax_core
 from jax._src import effects
 from jax._src import linear_util as lu
 from jax._src import state
+from jax._src import tree_util
 from jax._src.interpreters import ad
 from jax._src.interpreters import batching
 from jax._src.interpreters import mlir
@@ -45,6 +45,7 @@ from jax._src.util import (
     safe_zip,
     split_list,
     tuple_insert,
+    unzip2,
     weakref_lru_cache,
 )
 import jax.numpy as jnp
@@ -848,6 +849,7 @@ def pallas_call_checkify_rule(error: checkify.Error,
   # for the new error inputs and outputs.
   scalar_avals = map(checkify.get_shaped_aval, scalars)
   error_block_specs = [no_block_spec] * num_err_vals
+  error_paths, _ = unzip2(tree_util.tree_flatten_with_path(error_block_specs)[0])
   grid_avals = [
       jax_core.ShapedArray((), jnp.dtype("int32"))] * len(grid_mapping.grid)
   # TODO(justinfu): Place these in device-specific scalar memory.
@@ -862,8 +864,9 @@ def pallas_call_checkify_rule(error: checkify.Error,
             (*grid_avals, *scalar_ref_avals),
             in_tree=grid_tree,
             grid=grid_mapping.grid,
-            mapped_dims=grid_mapping.mapped_dims),
-        error_block_specs, error_memref_aval)
+            mapped_dims=grid_mapping.mapped_dims,
+            what="error"),
+        error_block_specs, error_paths, error_memref_aval)
   input_block_mappings, output_block_mappings = split_list(
       grid_mapping.block_mappings, [num_kernel_inputs,])
   grid_mapping_with_error = grid_mapping.replace(
@@ -893,10 +896,16 @@ def pallas_call_checkify_rule(error: checkify.Error,
 checkify.error_checks[pallas_call_p] = pallas_call_checkify_rule
 
 @weakref_lru_cache
-def _trace_to_jaxpr(fun: Callable, grid_spec: GridSpec, flat_in_avals,
-                    flat_out_avals, in_tree, out_tree, interpret: bool):
-  avals, grid_mapping = grid_spec.get_grid_mapping(flat_in_avals, in_tree,
-                                                   flat_out_avals, out_tree)
+def _trace_to_jaxpr(fun: Callable, grid_spec: GridSpec,
+                    flat_in_avals: Sequence[jax_core.AbstractValue],
+                    flat_out_avals: Sequence[jax_core.AbstractValue],
+                    in_tree: tree_util.PyTreeDef,
+                    in_paths: Sequence[tree_util.KeyPath],
+                    out_tree: tree_util.PyTreeDef,
+                    out_paths: Sequence[tree_util.KeyPath],
+                    interpret: bool):
+  avals, grid_mapping = grid_spec.get_grid_mapping(flat_in_avals, in_tree, in_paths,
+                                                   flat_out_avals, out_tree, out_paths)
   if interpret:
     avals = jax.tree_util.tree_map(_logical_aval_to_interpret_mode_aval, avals)
   jaxpr_flat_avals, jaxpr_in_tree = tree_util.tree_flatten(avals)
@@ -1058,19 +1067,25 @@ def pallas_call(
   grid_spec, dynamic_grid_bounds = grid_spec.unzip_dynamic_grid_bounds()
   if isinstance(out_shape, list):
     out_shape = tuple(out_shape)
-  flat_out_shapes, out_tree = tree_util.tree_flatten(out_shape)
-  flat_out_shapes = [jax.ShapeDtypeStruct(x.shape, x.dtype)
+  flat_out_shapes_with_paths, out_tree = tree_util.tree_flatten_with_path(out_shape)
+  out_paths, flat_out_shapes = unzip2(flat_out_shapes_with_paths)
+  flat_out_shapes = [jax.ShapeDtypeStruct(x.shape, x.dtype)  # type: ignore
                      for x in flat_out_shapes]
   @jax.jit
   def wrapped(*args):
-    flat_args, in_tree = tree_util.tree_flatten(args)
+    flat_args_with_paths, in_tree = tree_util.tree_flatten_with_path(args)
+    in_paths, flat_args = unzip2(flat_args_with_paths)
     flat_in_avals = tuple(jax_core.raise_to_shaped(jax_core.get_aval(a))
                           for a in flat_args)
     flat_out_avals = tuple(jax_core.ShapedArray(v.shape, v.dtype)
                            for v in flat_out_shapes)
-    grid_mapping, jaxpr, consts, _ = _trace_to_jaxpr(
-        f, grid_spec, flat_in_avals, flat_out_avals, in_tree,
-        out_tree, interpret=interpret)
+    grid_mapping, jaxpr, consts, f_out_tree = _trace_to_jaxpr(
+        f, grid_spec, flat_in_avals, flat_out_avals, in_tree, in_paths,
+        out_tree, out_paths, interpret=interpret)
+    if f_out_tree != tree_util.tree_flatten(None)[1]:
+      raise ValueError(
+          "The kernel function in a pallas_call should return None. "
+          f"Found a PyTree: {f_out_tree}")
     out_flat = pallas_call_p.bind(
         *dynamic_grid_bounds, *consts, *flat_args,
         jaxpr=jaxpr, name=name,
diff --git a/jax/_src/pjit.py b/jax/_src/pjit.py
index 0f21cb314..3e56119c2 100644
--- a/jax/_src/pjit.py
+++ b/jax/_src/pjit.py
@@ -1206,11 +1206,7 @@ def explain_tracing_cache_miss(
     p(f"  never seen input pytree{in_tree_str}")
     dont_match = [t for t, *_ in seen_keys if t != in_tree]
     closest_tree = min(dont_match, key=lambda t: abs(t.num_leaves - in_tree.num_leaves))
-    # TODO(mattjj): make equality_errors not print type name, avoid metaclass
-    leaf = type('LeafMeta', (type,), dict(__repr__=lambda _: 'leaf'))('Leaf', (), {})()
-    this_dummy = tree_unflatten(in_tree, [leaf] * in_tree.num_leaves)
-    close_dummy = tree_unflatten(closest_tree, [leaf] * closest_tree.num_leaves)  # type: ignore
-    errs = list(tree_util.equality_errors(this_dummy, close_dummy))
+    errs = list(tree_util.equality_errors_pytreedef(in_tree, closest_tree))  # type: ignore[arg-type]
     p(f"  closest seen input pytree has {len(errs)} mismatches, including:")
     for path, thing1, thing2, explanation in errs:
       fst, *path = path  # type: ignore
diff --git a/jax/_src/stages.py b/jax/_src/stages.py
index 874ef8834..34a573abd 100644
--- a/jax/_src/stages.py
+++ b/jax/_src/stages.py
@@ -43,7 +43,6 @@ from jax._src import config
 from jax._src import source_info_util
 from jax._src import traceback_util
 from jax._src import tree_util
-from jax._src.tree_util import tree_unflatten, keystr
 from jax._src import util
 from jax._src.sharding_impls import is_unspecified_or_auto
 from jax._src.layout import Layout
@@ -590,11 +589,7 @@ class Compiled(Stage):
           f"keyword arguments, but called with keyword arguments: {kws}")
     args_flat, in_tree = tree_util.tree_flatten((args, kwargs))
     if in_tree != params.in_tree:
-      leaf = PytreeLeaf()
-      this_dummy = tree_unflatten(in_tree, [leaf] * in_tree.num_leaves)
-      other_dummy = tree_unflatten(
-          params.in_tree, [leaf] * params.in_tree.num_leaves)
-      errs = list(tree_util.equality_errors(this_dummy, other_dummy))
+      errs = list(tree_util.equality_errors_pytreedef(in_tree, params.in_tree))
       msg = []
       msg.append(
           "Function compiled with input pytree does not match the input pytree"
@@ -603,7 +598,7 @@ class Compiled(Stage):
         fst, *rest = path
         base = ['args', 'kwargs'][fst.idx]
         msg.append(
-            f"    * at {base}{keystr(tuple(rest))}, seen {thing2} but now"
+            f"    * at {base}{tree_util.keystr(tuple(rest))}, seen {thing2} but now"
             f" given {thing1}, so {explanation}")
       raise TypeError('\n'.join(msg))
     try:
@@ -641,10 +636,6 @@ class Compiled(Stage):
     return self._call(*args, **kwargs)
 
 
-class PytreeLeaf:
-  def __repr__(self): return "pytree leaf"
-
-
 class Lowered(Stage):
   """Lowering of a function specialized to argument types and values.
 
diff --git a/jax/_src/tree_util.py b/jax/_src/tree_util.py
index 32f59b1df..a33a43ab6 100644
--- a/jax/_src/tree_util.py
+++ b/jax/_src/tree_util.py
@@ -621,7 +621,7 @@ def equality_errors(
   """Helper to describe structural differences between two pytrees.
 
   Args:
-    tree1, tree2: pytrees to compare.
+    tree1, tree2: pytrees known to have different structure.
 
   Usage:
 
@@ -636,6 +636,15 @@ def equality_errors(
   """
   yield from _equality_errors((), tree1, tree2, is_leaf)
 
+def equality_errors_pytreedef(
+    tree1: PyTreeDef,
+    tree2: PyTreeDef) -> Iterable[tuple[KeyPath, str, str, str]]:
+  """Like `equality_errors` but invoked on PyTreeDef."""
+  # TODO(mattjj): make equality_errors not print type name, avoid metaclass
+  leaf = type("LeafMeta", (type,), dict(__repr__=lambda _: "pytree leaf"))("Leaf", (), {})()
+  return equality_errors(tree_unflatten(tree1, [leaf] * tree1.num_leaves),
+                         tree_unflatten(tree2, [leaf] * tree2.num_leaves))
+
 # TODO(mattjj): maybe share some logic with _prefix_error?
 def _equality_errors(path, t1, t2, is_leaf):
   # If both are leaves, this isn't a structure equality error.
diff --git a/tests/pallas/pallas_test.py b/tests/pallas/pallas_test.py
index 876cbc52c..d5c927b5b 100644
--- a/tests/pallas/pallas_test.py
+++ b/tests/pallas/pallas_test.py
@@ -16,6 +16,7 @@ import contextlib
 import functools
 import itertools
 import os
+import re
 import sys
 
 os.environ["XLA_PYTHON_CLIENT_MEM_FRACTION"] = "0.5"
@@ -228,6 +229,27 @@ class PallasCallTest(PallasTest):
     for i in range(5):
       np.testing.assert_allclose(index(x, i), x[i])
 
+  def test_pallas_call_no_outputs(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref: None, ())
+    self.assertAllClose((), f(a))
+
+  def test_pallas_call_out_shape_is_singleton_tuple(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=(a,))
+    res = f(a)
+    self.assertIsInstance(res, tuple)
+    self.assertLen(res, 1)
+
+  def test_pallas_call_out_shape_is_list(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=[a])
+    res = f(a)
+    # TODO(necula): we normalize out_shape to a tuple, we shouldn't.
+    self.assertIsInstance(res, tuple)
+
   def test_hoisted_consts(self):
     # See https://github.com/google/jax/issues/21557.
     x = jnp.zeros(32)
@@ -441,6 +463,112 @@ class PallasCallInterpreterTest(PallasCallTest):
   INTERPRET = True
 
 
+class ApiErrorTest(PallasTest):
+
+  def test_pallas_kernel_args_mismatch(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref: None,  # Missing o_ref
+                         out_shape=a)
+    with self.assertRaisesRegex(
+        TypeError,
+        "takes 1 positional argument but 2 were given"):
+      f(a)
+
+  @parameterized.named_parameters(
+      ("array", 0),
+      ("empty_tuple", ())
+  )
+  def test_pallas_call_error_kernel_returns_something(self, returns):
+    a = np.arange(256, dtype=np.int32)
+    # The kernel should not return anything
+    f = self.pallas_call(lambda x_ref, o1_ref, o2_ref: returns,
+                         out_shape=(a, a))
+    with self.assertRaisesRegex(
+        ValueError,
+        "The kernel function in a pallas_call should return None"):
+      f(a)
+
+  def test_pallas_call_in_specs_not_a_sequence(self):
+    a = np.arange(256, dtype=np.int32)
+    with self.assertRaisesRegex(
+        ValueError,
+        "`in_specs` must be a tuple or a list"):
+      _ = self.pallas_call(lambda x_ref, o1_ref: None,
+                           out_shape=a,
+                           in_specs=pl.BlockSpec((4,), lambda: 0))
+
+  def test_pallas_call_in_specs_mismatch_inputs(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=a,
+                         in_specs=[pl.BlockSpec((4,), lambda: 0),
+                                   pl.BlockSpec((4,), lambda: 0)])
+    with self.assertRaisesRegex(
+        ValueError,
+        re.compile("Pytree for `in_specs` and inputs do not match. "
+                   "There are 1 mismatches, including:"
+                   ".* at \\[1\\], `in_specs` is a pytree leaf but "
+                   "inputs is a.*", re.DOTALL)):
+      f(a, dict(a=a))
+
+  def test_pallas_call_index_map_wrong_number_of_arguments(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=a,
+                         in_specs=[pl.BlockSpec((4,), lambda i, j: 0)])
+    with self.assertRaisesRegex(
+        TypeError,
+        "missing 2 required positional arguments: 'i' and 'j'"):
+      f(a)
+
+  def test_pallas_call_index_map_wrong_number_of_results(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=a,
+                         in_specs=[pl.BlockSpec((4,), lambda: (0, 0))])
+    with self.assertRaisesRegex(
+        ValueError,
+        "Index map for input\\[0\\] must return 1 values to match .*Currently returning 2 values."):
+      f(a)
+
+  def test_pallas_call_out_specs_mismatch_shape(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=[a, a],
+                         out_specs=[pl.BlockSpec((6,), lambda i: i)])
+    with self.assertRaisesRegex(
+        ValueError,
+        re.compile("Pytree for `out_specs` and `out_shape` do not match. There are 1 mismatches, including:"
+         ".* `out_specs` is a tuple of length 1 but `out_shape` is a tuple of length 2.*", re.DOTALL)):
+      f(a)
+
+
+  def test_pallas_call_block_shape_ndim_mismatch(self):
+    a = np.arange(256, dtype=np.int32)
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=[a],
+                         in_specs=[pl.BlockSpec((1, 1), lambda: (0, 0))])
+    with self.assertRaisesRegex(
+        ValueError,
+        "Block shape for input\\[0\\] .* must have the same number of dimensions as the "
+        "array shape"):
+
+      f(a)
+
+    f = self.pallas_call(lambda x_ref, o1_ref: None,
+                         out_shape=[a],
+                         out_specs=[pl.BlockSpec((1, 1), lambda: 0)])
+    with self.assertRaisesRegex(
+        ValueError,
+        "Block shape for output\\[0\\] .* must have the same number of dimensions as the "
+        "array shape"):
+      f(a)
+
+
+class ApiErrorInterpreterTest(ApiErrorTest):
+  INTERPRET = True
+
+
 class PallasControlFlowTest(PallasTest):
 
   def setUp(self):
diff --git a/tests/pallas/tpu/pallas_call_test.py b/tests/pallas/tpu/pallas_call_test.py
index 92e518206..b85533146 100644
--- a/tests/pallas/tpu/pallas_call_test.py
+++ b/tests/pallas/tpu/pallas_call_test.py
@@ -115,6 +115,67 @@ class PallasCallScalarPrefetchTest(PallasTPUTest):
     )(s, x)
     np.testing.assert_array_equal(out, x)
 
+  def test_block_spec_with_wrong_block_shape_errors(self):
+    def body(x_ref, o_ref):
+      o_ref[...] = x_ref[...]
+
+    x = jnp.ones((16, 128))
+    with self.assertRaisesRegex(
+        ValueError,
+        'Block shape .* must have the same number of dimensions as the array shape .*'):
+      _ = pl.pallas_call(
+          body,
+          grid_spec=pltpu.PrefetchScalarGridSpec(
+              num_scalar_prefetch=0,
+              in_specs=[pl.BlockSpec((128,), lambda i: (i, 0))],  # WRONG
+              out_specs=pl.BlockSpec((8, 128,), lambda i: (i, 0)),
+              grid=(2,),
+          ),
+          out_shape=x,
+          interpret=self.interpret,
+      )(x)
+
+  def test_block_spec_with_index_map_that_accepts_wrong_number_of_args_errors(self):
+    def body(x_ref, o_ref):
+      o_ref[...] = x_ref[...]
+
+    x = jnp.ones((16, 128))
+    with self.assertRaisesRegex(
+        TypeError,
+        'missing 1 required positional argument: \'j\''):
+      _ = pl.pallas_call(
+          body,
+          grid_spec=pltpu.PrefetchScalarGridSpec(
+              num_scalar_prefetch=0,
+              in_specs=[pl.BlockSpec((8, 128,), lambda i, j: (i, 0))],  # WRONG
+              out_specs=pl.BlockSpec((8, 128,), lambda i: (i, 0),),
+              grid=(2,),
+          ),
+          out_shape=x,
+          interpret=self.interpret
+      )(x)
+
+  def test_block_spec_with_index_map_returns_wrong_number_of_values_errors(self):
+    def body(x_ref, o_ref):
+      o_ref[...] = x_ref[...]
+
+    x = jnp.ones((16, 128))
+    with self.assertRaisesRegex(
+        ValueError,
+        r'Index map for input\[0\] must return 2 values to match block_shape=\(8, 128\).'
+        ' Currently returning 1 values.'):
+      _ = pl.pallas_call(
+          body,
+          grid_spec=pltpu.PrefetchScalarGridSpec(
+              num_scalar_prefetch=0,
+              in_specs=[pl.BlockSpec((8, 128,), lambda i: (i,))],  # WRONG
+              out_specs=pl.BlockSpec((8, 128), lambda i: (i, 0)),
+              grid=(2,),
+          ),
+          out_shape=x,
+          interpret=self.interpret,
+      )(x)
+
   def test_vmap_scalar_prefetch(self):
     def body(_, x_ref, o_ref):
       o_ref[...] = x_ref[...]
@@ -138,8 +199,7 @@ class PallasCallScalarPrefetchTest(PallasTPUTest):
               out_specs=pl.BlockSpec(
                   (x.shape[0] // 8, x.shape[1]), lambda i, _: (i, 0)
               ),
-              grid=8,
-          ),
+              grid=8),
           interpret=self.interpret,
       )(s, x)
     np.testing.assert_allclose(
@@ -363,7 +423,7 @@ class PallasCallDynamicGridTest(PallasTPUTest):
       num_programs = pl.num_programs(0)
       self.assertIsInstance(num_programs, int)
       self.assertEqual(num_programs, 2)
-      return 0
+      return 0, 0
     pl.pallas_call(
         kernel,
         in_specs=[pl.BlockSpec((8, 128), x_index_map)],
diff --git a/tests/pallas/tpu/pallas_random_test.py b/tests/pallas/tpu/pallas_random_test.py
index c8db82179..e3d43125c 100644
--- a/tests/pallas/tpu/pallas_random_test.py
+++ b/tests/pallas/tpu/pallas_random_test.py
@@ -184,7 +184,7 @@ class BlockInvarianceTest(parameterized.TestCase):
 
     def make_kernel_body(index_map):
       def body(key_ref, o_ref):
-        key = key_ref[0, 0]
+        key = key_ref[...]
         samples = plrandom.sample_block(
             jax.random.uniform,
             key,
@@ -199,9 +199,7 @@ class BlockInvarianceTest(parameterized.TestCase):
 
     global_key = jax_random.key(0, impl="pallas_tpu")
     o_shape = jnp.ones((64, 512), dtype=jnp.float32)
-    key_spec = pl.BlockSpec(
-        (1, 1), lambda i, j: (0, 0), memory_space=pltpu.TPUMemorySpace.SMEM
-    )
+    key_spec = pl.BlockSpec(memory_space=pltpu.TPUMemorySpace.SMEM)
     out_spec = pl.BlockSpec((16, 128), lambda i, j: (i, j))
     result_16x128 = pl.pallas_call(
         make_kernel_body(index_map=lambda i, j: (i, j)),