diff --git a/src/awkward/_categorical.py b/src/awkward/_categorical.py
index ade1f74235..762e467128 100644
--- a/src/awkward/_categorical.py
+++ b/src/awkward/_categorical.py
@@ -28,7 +28,7 @@ def __eq__(self, other):
 
 class HashableList:
     def __init__(self, obj):
-        self.values = tuple(obj)
+        self.values = tuple(as_hashable(x) for x in obj)
         self.hash = hash((HashableList, *self.values))
 
     def __hash__(self):
diff --git a/src/awkward/_do.py b/src/awkward/_do.py
index 8b48cf3ad0..e2ead1919b 100644
--- a/src/awkward/_do.py
+++ b/src/awkward/_do.py
@@ -63,6 +63,7 @@ def recursively_apply(
             return_simplified,
             return_array,
             function_name,
+            regular_to_jagged,
         )
 
         if return_array:
diff --git a/src/awkward/_errors.py b/src/awkward/_errors.py
index bd357175a6..9c97481939 100644
--- a/src/awkward/_errors.py
+++ b/src/awkward/_errors.py
@@ -188,12 +188,11 @@ def any_backend_is_delayed(
             if backend is None:
                 # Is this an iterable object, and are we permitted to recurse?
                 if isinstance(obj, Collection) and depth != depth_limit:
-                    return self.any_backend_is_delayed(
+                    if self.any_backend_is_delayed(
                         obj, depth=depth + 1, depth_limit=depth_limit
-                    )
-                # Assume not delayed!
-                else:
-                    return False
+                    ):
+                        return True
+                # Assume not delayed! Continue checking remaining args.
             # Eager backends aren't delayed!
             elif backend.nplike.is_eager:
                 continue
diff --git a/src/awkward/prettyprint.py b/src/awkward/prettyprint.py
index 2ac5be8229..df9a29c05a 100644
--- a/src/awkward/prettyprint.py
+++ b/src/awkward/prettyprint.py
@@ -179,7 +179,8 @@ def valuestr_horiz(
 
                     custom = custom_str(current)
                     if custom is not None:
-                        strs = custom
+                        strs = [custom]
+                        cols_taken = len(custom)
 
                     if limit_cols - (for_comma + cols_taken) >= 0:
                         if which != 0:
@@ -196,7 +197,8 @@ def valuestr_horiz(
 
                     custom = custom_str(current)
                     if custom is not None:
-                        strs = custom
+                        strs = [custom]
+                        cols_taken = len(custom)
 
                     if limit_cols - (2 + cols_taken) >= 0:
                         back[:0] = strs
diff --git a/tests/test_4106_fix_core_misc.py b/tests/test_4106_fix_core_misc.py
new file mode 100644
index 0000000000..3815760b4d
--- /dev/null
+++ b/tests/test_4106_fix_core_misc.py
@@ -0,0 +1,137 @@
+# BSD 3-Clause License; see https://github.com/scikit-hep/awkward/blob/main/LICENSE
+
+from __future__ import annotations
+
+import numpy as np
+
+import awkward as ak
+from awkward._categorical import as_hashable
+from awkward._do import recursively_apply
+from awkward._errors import OperationErrorContext
+from awkward.prettyprint import Formatter
+
+
+def test_hashablelist_with_dict_elements_is_hashable():
+    """HashableList with dict elements used to raise TypeError: unhashable type 'dict'."""
+    obj = [{"x": 1}, {"x": 2}]
+    h = as_hashable(obj)
+    # Must be hashable and usable as a dict key
+    lookup = {h: "found"}
+    assert lookup[as_hashable(obj)] == "found"
+
+
+def test_categorical_equal_list_of_lists():
+    """Comparing categorical arrays whose categories are lists (different orders)."""
+    categories1 = ak.Array([[1, 2], [3, 4]])
+    categories2 = ak.Array([[3, 4], [1, 2]])  # reversed order
+    index1 = ak.index.Index64(np.array([0, 1, 0], dtype=np.int64))
+    index2 = ak.index.Index64(np.array([0, 0, 1], dtype=np.int64))
+    cat1 = ak.contents.IndexedArray(
+        index1, categories1.layout, parameters={"__array__": "categorical"}
+    )
+    cat2 = ak.contents.IndexedArray(
+        index2, categories2.layout, parameters={"__array__": "categorical"}
+    )
+    # cat1 values: [1,2] [3,4] [1,2]; cat2 values: [3,4] [3,4] [1,2]
+    result = (ak.Array(cat1) == ak.Array(cat2)).to_list()
+    assert result == [False, True, True]
+
+
+def test_any_backend_is_delayed_continues_after_unknown_object():
+    """A plain (non-array) item before an eager array must not prevent detection.
+
+    Before the fix, encountering an unrecognised object caused an unconditional
+    return False, so any arrays later in the argument list were never checked.
+    """
+    ctx = OperationErrorContext.__new__(OperationErrorContext)
+    eager = ak.Array([1, 2, 3])
+    assert ctx.any_backend_is_delayed([42, eager]) is False
+
+
+def test_any_backend_is_delayed_nested_non_delayed_continues():
+    """Nested iterable returning False from recursion must not short-circuit outer loop."""
+    ctx = OperationErrorContext.__new__(OperationErrorContext)
+    eager = ak.Array([1, 2])
+    result = ctx.any_backend_is_delayed([[42], eager], depth_limit=2)
+    assert result is False
+
+
+def _make_custom_str_array(n=5):
+    class MyPoint(ak.Record):
+        def __str__(self):
+            return "POINT"
+
+    return ak.Array(
+        [{"x": i} for i in range(n)],
+        behavior={"MyPoint": MyPoint},
+        with_name="MyPoint",
+    )
+
+
+def test_prettyprint_custom_str_not_spliced():
+    """custom_str result must be treated as a single token, not spliced char-by-char."""
+    from awkward.prettyprint import valuestr_horiz
+
+    arr = _make_custom_str_array(5)
+    cols_taken, strs = valuestr_horiz(arr, 80, Formatter())
+
+    # Before the fix, front.extend(str) iterated characters; "POINT" would appear
+    # as individual letters.  Now each token must be "POINT" in full.
+    single_letters_from_point = set("POINT")
+    for s in strs:
+        if len(s) == 1 and s in single_letters_from_point:
+            raise AssertionError(
+                f"custom_str was spliced char-by-char: found {s!r} in {strs}"
+            )
+    # cols_taken must match the actual rendered width
+    joined = "".join(strs)
+    assert len(joined) == cols_taken
+
+
+def test_prettyprint_repr_does_not_explode():
+    """repr() of an array with custom-str records must not raise or overflow."""
+    arr = _make_custom_str_array(5)
+    result = repr(arr)
+    assert isinstance(result, str)
+    assert len(result) < 500
+
+
+def test_recursively_apply_record_regular_to_jagged_forwarded():
+    """recursively_apply with regular_to_jagged=True on a Record must forward the arg."""
+    from awkward.contents.recordarray import RecordArray
+    from awkward.record import Record as LowRecord
+
+    regular = ak.to_regular(ak.Array([[1, 2], [3, 4]]))
+    ra = RecordArray([regular.layout], ["vals"])
+    low_rec = LowRecord(ra, 0)
+
+    seen_options = []
+
+    def action(layout, **kwargs):
+        seen_options.append(kwargs.get("options", {}))
+        return None
+
+    recursively_apply(low_rec, action, regular_to_jagged=True)
+    assert any(opts.get("regular_to_jagged") is True for opts in seen_options)
+
+
+def test_recursively_apply_record_regular_to_jagged_converts_type():
+    """With regular_to_jagged=True, RegularArray inside a Record is converted."""
+    from awkward.contents.recordarray import RecordArray
+    from awkward.record import Record as LowRecord
+
+    regular = ak.to_regular(ak.Array([[1, 2], [3, 4]]))
+    ra = RecordArray([regular.layout], ["vals"])
+    low_rec = LowRecord(ra, 0)
+
+    seen_types = []
+
+    def action(layout, **kwargs):
+        seen_types.append(type(layout).__name__)
+        return None
+
+    recursively_apply(low_rec, action, regular_to_jagged=True)
+
+    # RegularArray should be converted to ListOffsetArray
+    assert "RegularArray" not in seen_types, f"seen: {seen_types}"
+    assert "ListOffsetArray" in seen_types