diff --git a/bson/json_util.py b/bson/json_util.py
index a171327ead..ecae103b55 100644
--- a/bson/json_util.py
+++ b/bson/json_util.py
@@ -617,25 +617,28 @@ def _parse_canonical_datetime(
         raise TypeError(f"Bad $date, extra field(s): {doc}")
     # mongoexport 2.6 and newer
     if isinstance(dtm, str):
-        # Parse offset
-        if dtm[-1] == "Z":
-            dt = dtm[:-1]
-            offset = "Z"
-        elif dtm[-6] in ("+", "-") and dtm[-3] == ":":
-            # (+|-)HH:MM
-            dt = dtm[:-6]
-            offset = dtm[-6:]
-        elif dtm[-5] in ("+", "-"):
-            # (+|-)HHMM
-            dt = dtm[:-5]
-            offset = dtm[-5:]
-        elif dtm[-3] in ("+", "-"):
-            # (+|-)HH
-            dt = dtm[:-3]
-            offset = dtm[-3:]
-        else:
-            dt = dtm
-            offset = ""
+        try:
+            # Parse offset
+            if dtm[-1] == "Z":
+                dt = dtm[:-1]
+                offset = "Z"
+            elif dtm[-6] in ("+", "-") and dtm[-3] == ":":
+                # (+|-)HH:MM
+                dt = dtm[:-6]
+                offset = dtm[-6:]
+            elif dtm[-5] in ("+", "-"):
+                # (+|-)HHMM
+                dt = dtm[:-5]
+                offset = dtm[-5:]
+            elif dtm[-3] in ("+", "-"):
+                # (+|-)HH
+                dt = dtm[:-3]
+                offset = dtm[-3:]
+            else:
+                dt = dtm
+                offset = ""
+        except IndexError as exc:
+            raise ValueError(f"time data {dtm!r} does not match ISO-8601 datetime format") from exc
 
         # Parse the optional factional seconds portion.
         dot_index = dt.rfind(".")
@@ -848,7 +851,7 @@ def _encode_datetimems(obj: Any, json_options: JSONOptions) -> dict:
     ):
         return _encode_datetime(obj.as_datetime(), json_options)
     elif json_options.datetime_representation == DatetimeRepresentation.LEGACY:
-        return {"$date": str(int(obj))}
+        return {"$date": int(obj)}
     return {"$date": {"$numberLong": str(int(obj))}}
 
 
diff --git a/doc/changelog.rst b/doc/changelog.rst
index bd4eafe3ef..d9e6cc3f5b 100644
--- a/doc/changelog.rst
+++ b/doc/changelog.rst
@@ -28,6 +28,11 @@ PyMongo 4.11 brings a number of changes including:
   :meth:`~pymongo.asynchronous.mongo_client.AsyncMongoClient.bulk_write` now throw an error
   when ``ordered=True`` or ``verboseResults=True`` are used with unacknowledged writes.
   These are unavoidable breaking changes.
+- Fixed a bug in :const:`bson.json_util.dumps` where a :class:`bson.datetime_ms.DatetimeMS` would
+  be incorrectly encoded as ``'{"$date": "X"}'`` instead of ``'{"$date": X}'`` when using the
+  legacy MongoDB Extended JSON datetime representation.
+- Fixed a bug where :const:`bson.json_util.loads` would raise an IndexError when parsing an invalid
+  ``"$date"`` instead of a ValueError.
 
 Issues Resolved
 ...............
diff --git a/test/test_json_util.py b/test/test_json_util.py
index 3a40c174e8..821ca76da0 100644
--- a/test/test_json_util.py
+++ b/test/test_json_util.py
@@ -137,7 +137,7 @@ def test_datetime(self):
             '{"dt": { "$date" : "1970-01-01T00:00:00.000Z"}}',
             '{"dt": { "$date" : "1970-01-01T00:00:00.000000Z"}}',
             '{"dt": { "$date" : "1970-01-01T00:00:00Z"}}',
-            '{"dt": {"$date": "1970-01-01T00:00:00.000"}}',
+            '{"dt": { "$date" : "1970-01-01T00:00:00.000"}}',
             '{"dt": { "$date" : "1970-01-01T00:00:00"}}',
             '{"dt": { "$date" : "1970-01-01T00:00:00.000000"}}',
             '{"dt": { "$date" : "1969-12-31T16:00:00.000-0800"}}',
@@ -282,9 +282,9 @@ def test_datetime_ms(self):
         opts = JSONOptions(
             datetime_representation=DatetimeRepresentation.LEGACY, json_mode=JSONMode.LEGACY
         )
-        self.assertEqual('{"x": {"$date": "-1"}}', json_util.dumps(dat_min, json_options=opts))
+        self.assertEqual('{"x": {"$date": -1}}', json_util.dumps(dat_min, json_options=opts))
         self.assertEqual(
-            '{"x": {"$date": "' + str(int(dat_max["x"])) + '"}}',
+            '{"x": {"$date": ' + str(int(dat_max["x"])) + "}}",
             json_util.dumps(dat_max, json_options=opts),
         )
 
@@ -317,6 +317,25 @@ def test_datetime_ms(self):
             json_util.loads(json_util.dumps(dat_max), json_options=opts)["x"],
         )
 
+    def test_parse_invalid_date(self):
+        # These cases should raise ValueError, not IndexError.
+        for invalid in [
+            '{"dt": { "$date" : "1970-01-01T00:00:"}}',
+            '{"dt": { "$date" : "1970-01-01T01:00"}}',
+            '{"dt": { "$date" : "1970-01-01T01:"}}',
+            '{"dt": { "$date" : "1970-01-01T01"}}',
+            '{"dt": { "$date" : "1970-01-01T"}}',
+            '{"dt": { "$date" : "1970-01-01"}}',
+            '{"dt": { "$date" : "1970-01-"}}',
+            '{"dt": { "$date" : "1970-01"}}',
+            '{"dt": { "$date" : "1970-"}}',
+            '{"dt": { "$date" : "1970"}}',
+            '{"dt": { "$date" : "1"}}',
+            '{"dt": { "$date" : ""}}',
+        ]:
+            with self.assertRaisesRegex(ValueError, "does not match"):
+                json_util.loads(invalid)
+
     def test_regex_object_hook(self):
         # Extended JSON format regular expression.
         pat = "a*b"