diff --git a/changelog.d/16526.misc b/changelog.d/16526.misc
new file mode 100644
index 0000000000..93ceaeafc9
--- /dev/null
+++ b/changelog.d/16526.misc
@@ -0,0 +1 @@
+Improve type hints.
diff --git a/synapse/util/file_consumer.py b/synapse/util/file_consumer.py
index 46771a401b..26b46be5e1 100644
--- a/synapse/util/file_consumer.py
+++ b/synapse/util/file_consumer.py
@@ -13,7 +13,7 @@
 # limitations under the License.
 
 import queue
-from typing import BinaryIO, Optional, Union, cast
+from typing import Any, BinaryIO, Optional, Union, cast
 
 from twisted.internet import threads
 from twisted.internet.defer import Deferred
@@ -58,7 +58,9 @@ class BackgroundFileConsumer:
         self._bytes_queue: queue.Queue[Optional[bytes]] = queue.Queue()
 
         # Deferred that is resolved when finished writing
-        self._finished_deferred: Optional[Deferred[None]] = None
+        #
+        # This is really Deferred[None], but mypy doesn't seem to like that.
+        self._finished_deferred: Optional[Deferred[Any]] = None
 
         # If the _writer thread throws an exception it gets stored here.
         self._write_exception: Optional[Exception] = None
@@ -80,9 +82,13 @@ class BackgroundFileConsumer:
         self.streaming = streaming
         self._finished_deferred = run_in_background(
             threads.deferToThreadPool,
-            self._reactor,
-            self._reactor.getThreadPool(),
-            self._writer,
+            # mypy seems to get confused with the chaining of ParamSpec from
+            # run_in_background to deferToThreadPool.
+            #
+            # For Twisted trunk, ignore arg-type; for Twisted release ignore unused-ignore.
+            self._reactor,  # type: ignore[arg-type,unused-ignore]
+            self._reactor.getThreadPool(),  # type: ignore[arg-type,unused-ignore]
+            self._writer,  # type: ignore[arg-type,unused-ignore]
         )
         if not streaming:
             self._producer.resumeProducing()
diff --git a/tests/handlers/test_appservice.py b/tests/handlers/test_appservice.py
index 867dbd6001..c888d1ff01 100644
--- a/tests/handlers/test_appservice.py
+++ b/tests/handlers/test_appservice.py
@@ -156,6 +156,7 @@ class AppServiceHandlerTestCase(unittest.TestCase):
         result = self.successResultOf(
             defer.ensureDeferred(self.handler.query_room_alias_exists(room_alias))
         )
+        assert result is not None
 
         self.mock_as_api.query_alias.assert_called_once_with(
             interested_service, room_alias_str
diff --git a/tests/http/server/_base.py b/tests/http/server/_base.py
index 36472e57a8..d524c183f8 100644
--- a/tests/http/server/_base.py
+++ b/tests/http/server/_base.py
@@ -335,7 +335,7 @@ class Deferred__next__Patch:
         self._request_number = request_number
         self._seen_awaits = seen_awaits
 
-        self._original_Deferred___next__ = Deferred.__next__
+        self._original_Deferred___next__ = Deferred.__next__  # type: ignore[misc,unused-ignore]
 
         # The number of `await`s on `Deferred`s we have seen so far.
         self.awaits_seen = 0
diff --git a/tests/http/test_matrixfederationclient.py b/tests/http/test_matrixfederationclient.py
index ab94f3f67a..bf1d287699 100644
--- a/tests/http/test_matrixfederationclient.py
+++ b/tests/http/test_matrixfederationclient.py
@@ -70,7 +70,7 @@ class FederationClientTests(HomeserverTestCase):
         """
 
         @defer.inlineCallbacks
-        def do_request() -> Generator["Deferred[object]", object, object]:
+        def do_request() -> Generator["Deferred[Any]", object, object]:
             with LoggingContext("one") as context:
                 fetch_d = defer.ensureDeferred(
                     self.cl.get_json("testserv:8008", "foo/bar")
diff --git a/tests/unittest.py b/tests/unittest.py
index 99ad02eb06..79c47fc3cc 100644
--- a/tests/unittest.py
+++ b/tests/unittest.py
@@ -30,6 +30,7 @@ from typing import (
     Generic,
     Iterable,
     List,
+    Mapping,
     NoReturn,
     Optional,
     Tuple,
@@ -251,7 +252,7 @@ class TestCase(unittest.TestCase):
             except AssertionError as e:
                 raise (type(e))(f"Assert error for '.{key}':") from e
 
-    def assert_dict(self, required: dict, actual: dict) -> None:
+    def assert_dict(self, required: Mapping, actual: Mapping) -> None:
         """Does a partial assert of a dict.
 
         Args: