diff --git a/changelog.d/14605.bugfix b/changelog.d/14605.bugfix
new file mode 100644
index 000000000000..cb95a87d9219
--- /dev/null
+++ b/changelog.d/14605.bugfix
@@ -0,0 +1 @@
+Return spec-compliant JSON errors when unknown endpoints are requested.
diff --git a/docs/admin_api/media_admin_api.md b/docs/admin_api/media_admin_api.md
index 7f8c8e22c1a0..30833f31091b 100644
--- a/docs/admin_api/media_admin_api.md
+++ b/docs/admin_api/media_admin_api.md
@@ -235,6 +235,14 @@ The following fields are returned in the JSON response body:
 
 Request:
 
+```
+POST /_synapse/admin/v1/media/delete?before_ts=<before_ts>
+
+{}
+```
+
+*Deprecated in Synapse v1.78.0:* This API is available at the deprecated endpoint:
+
 ```
 POST /_synapse/admin/v1/media/<server_name>/delete?before_ts=<before_ts>
 
@@ -243,7 +251,7 @@ POST /_synapse/admin/v1/media/<server_name>/delete?before_ts=<before_ts>
 
 URL Parameters
 
-* `server_name`: string - The name of your local server (e.g `matrix.org`).
+* `server_name`: string - The name of your local server (e.g `matrix.org`). *Deprecated in Synapse v1.78.0.*
 * `before_ts`: string representing a positive integer - Unix timestamp in milliseconds.
 Files that were last used before this timestamp will be deleted. It is the timestamp of
 last access, not the timestamp when the file was created.
diff --git a/docs/upgrade.md b/docs/upgrade.md
index bc143444bed6..15167b8c5825 100644
--- a/docs/upgrade.md
+++ b/docs/upgrade.md
@@ -88,6 +88,15 @@ process, for example:
     dpkg -i matrix-synapse-py3_1.3.0+stretch1_amd64.deb
     ```
 
+# Upgrading to v1.78.0
+
+## Deprecate the `/_synapse/admin/v1/media/<server_name>/delete` admin API
+
+Synapse 1.78.0 replaces the `/_synapse/admin/v1/media/<server_name>/delete`
+admin API with an identical endpoint at `/_synapse/admin/v1/media/delete`. Please
+update your tooling to use the new endpoint. The deprecated version will be removed
+in a future release.
+
 # Upgrading to v1.76.0
 
 ## Faster joins are enabled by default
@@ -137,6 +146,7 @@ and then do `pip install matrix-synapse[user-search]` for a PyPI install.
 Docker images and Debian packages need nothing specific as they already
 include or specify ICU as an explicit dependency.
 
+
 # Upgrading to v1.73.0
 
 ## Legacy Prometheus metric names have now been removed
diff --git a/synapse/http/server.py b/synapse/http/server.py
index 2563858f3cdf..9314454af106 100644
--- a/synapse/http/server.py
+++ b/synapse/http/server.py
@@ -30,7 +30,6 @@
     Iterable,
     Iterator,
     List,
-    NoReturn,
     Optional,
     Pattern,
     Tuple,
@@ -340,7 +339,8 @@ async def _async_render(self, request: SynapseRequest) -> Optional[Tuple[int, An
 
             return callback_return
 
-        return _unrecognised_request_handler(request)
+        # A request with an unknown method (for a known endpoint) was received.
+        raise UnrecognizedRequestError(code=405)
 
     @abc.abstractmethod
     def _send_response(
@@ -396,7 +396,6 @@ def _send_error_response(
 
 @attr.s(slots=True, frozen=True, auto_attribs=True)
 class _PathEntry:
-    pattern: Pattern
     callback: ServletCallback
     servlet_classname: str
 
@@ -425,13 +424,14 @@ def __init__(
     ):
         super().__init__(canonical_json, extract_context)
         self.clock = hs.get_clock()
-        self.path_regexs: Dict[bytes, List[_PathEntry]] = {}
+        # Map of path regex -> method -> callback.
+        self._routes: Dict[Pattern[str], Dict[bytes, _PathEntry]] = {}
         self.hs = hs
 
     def register_paths(
         self,
         method: str,
-        path_patterns: Iterable[Pattern],
+        path_patterns: Iterable[Pattern[str]],
         callback: ServletCallback,
         servlet_classname: str,
     ) -> None:
@@ -455,8 +455,8 @@ def register_paths(
 
         for path_pattern in path_patterns:
             logger.debug("Registering for %s %s", method, path_pattern.pattern)
-            self.path_regexs.setdefault(method_bytes, []).append(
-                _PathEntry(path_pattern, callback, servlet_classname)
+            self._routes.setdefault(path_pattern, {})[method_bytes] = _PathEntry(
+                callback, servlet_classname
             )
 
     def _get_handler_for_request(
@@ -478,14 +478,17 @@ def _get_handler_for_request(
 
         # Loop through all the registered callbacks to check if the method
         # and path regex match
-        for path_entry in self.path_regexs.get(request_method, []):
-            m = path_entry.pattern.match(request_path)
+        for path_pattern, methods in self._routes.items():
+            m = path_pattern.match(request_path)
             if m:
-                # We found a match!
+                # We found a matching path!
+                path_entry = methods.get(request_method)
+                if not path_entry:
+                    raise UnrecognizedRequestError(code=405)
                 return path_entry.callback, path_entry.servlet_classname, m.groupdict()
 
-        # Huh. No one wanted to handle that? Fiiiiiine. Send 400.
-        return _unrecognised_request_handler, "unrecognised_request_handler", {}
+        # Huh. No one wanted to handle that? Fiiiiiine.
+        raise UnrecognizedRequestError(code=404)
 
     async def _async_render(self, request: SynapseRequest) -> Tuple[int, Any]:
         callback, servlet_classname, group_dict = self._get_handler_for_request(request)
@@ -567,19 +570,6 @@ def render_GET(self, request: Request) -> bytes:
         return super().render_GET(request)
 
 
-def _unrecognised_request_handler(request: Request) -> NoReturn:
-    """Request handler for unrecognised requests
-
-    This is a request handler suitable for return from
-    _get_handler_for_request. It actually just raises an
-    UnrecognizedRequestError.
-
-    Args:
-        request: Unused, but passed in to match the signature of ServletCallback.
-    """
-    raise UnrecognizedRequestError(code=404)
-
-
 class UnrecognizedRequestResource(resource.Resource):
     """
     Similar to twisted.web.resource.NoResource, but returns a JSON 404 with an
diff --git a/synapse/rest/admin/media.py b/synapse/rest/admin/media.py
index 0d072c42a7aa..c134ccfb3d3c 100644
--- a/synapse/rest/admin/media.py
+++ b/synapse/rest/admin/media.py
@@ -15,7 +15,7 @@
 
 import logging
 from http import HTTPStatus
-from typing import TYPE_CHECKING, Tuple
+from typing import TYPE_CHECKING, Optional, Tuple
 
 from synapse.api.constants import Direction
 from synapse.api.errors import Codes, NotFoundError, SynapseError
@@ -285,7 +285,12 @@ class DeleteMediaByDateSize(RestServlet):
     timestamp and size.
     """
 
-    PATTERNS = admin_patterns("/media/(?P<server_name>[^/]*)/delete$")
+    PATTERNS = [
+        *admin_patterns("/media/delete$"),
+        # This URL kept around for legacy reasons, it is undesirable since it
+        # overlaps with the DeleteMediaByID servlet.
+        *admin_patterns("/media/(?P<server_name>[^/]*)/delete$"),
+    ]
 
     def __init__(self, hs: "HomeServer"):
         self.store = hs.get_datastores().main
@@ -294,7 +299,7 @@ def __init__(self, hs: "HomeServer"):
         self.media_repository = hs.get_media_repository()
 
     async def on_POST(
-        self, request: SynapseRequest, server_name: str
+        self, request: SynapseRequest, server_name: Optional[str] = None
     ) -> Tuple[int, JsonDict]:
         await assert_requester_is_admin(self.auth, request)
 
@@ -322,7 +327,8 @@ async def on_POST(
                 errcode=Codes.INVALID_PARAM,
             )
 
-        if self.server_name != server_name:
+        # This check is useless, we keep it for the legacy endpoint only.
+        if server_name is not None and self.server_name != server_name:
             raise SynapseError(HTTPStatus.BAD_REQUEST, "Can only delete local media")
 
         logging.info(
@@ -489,6 +495,8 @@ def register_servlets_for_media_repo(hs: "HomeServer", http_server: HttpServer)
     ProtectMediaByID(hs).register(http_server)
     UnprotectMediaByID(hs).register(http_server)
     ListMediaInRoom(hs).register(http_server)
-    DeleteMediaByID(hs).register(http_server)
+    # XXX DeleteMediaByDateSize must be registered before DeleteMediaByID as
+    #     their URL routes overlap.
     DeleteMediaByDateSize(hs).register(http_server)
+    DeleteMediaByID(hs).register(http_server)
     UserMediaRestServlet(hs).register(http_server)
diff --git a/synapse/rest/client/room_keys.py b/synapse/rest/client/room_keys.py
index f7081f638e51..4e7ffdb5551e 100644
--- a/synapse/rest/client/room_keys.py
+++ b/synapse/rest/client/room_keys.py
@@ -259,6 +259,32 @@ def __init__(self, hs: "HomeServer"):
         self.auth = hs.get_auth()
         self.e2e_room_keys_handler = hs.get_e2e_room_keys_handler()
 
+    async def on_GET(self, request: SynapseRequest) -> Tuple[int, JsonDict]:
+        """
+        Retrieve the version information about the most current backup version (if any)
+
+        It takes out an exclusive lock on this user's room_key backups, to ensure
+        clients only upload to the current backup.
+
+        Returns 404 if the given version does not exist.
+
+        GET /room_keys/version HTTP/1.1
+        {
+            "version": "12345",
+            "algorithm": "m.megolm_backup.v1",
+            "auth_data": "dGhpcyBzaG91bGQgYWN0dWFsbHkgYmUgZW5jcnlwdGVkIGpzb24K"
+        }
+        """
+        requester = await self.auth.get_user_by_req(request, allow_guest=False)
+        user_id = requester.user.to_string()
+
+        try:
+            info = await self.e2e_room_keys_handler.get_version_info(user_id)
+        except SynapseError as e:
+            if e.code == 404:
+                raise SynapseError(404, "No backup found", Codes.NOT_FOUND)
+        return 200, info
+
     async def on_POST(self, request: SynapseRequest) -> Tuple[int, JsonDict]:
         """
         Create a new backup version for this user's room_keys with the given
@@ -301,7 +327,7 @@ async def on_POST(self, request: SynapseRequest) -> Tuple[int, JsonDict]:
 
 
 class RoomKeysVersionServlet(RestServlet):
-    PATTERNS = client_patterns("/room_keys/version(/(?P<version>[^/]+))?$")
+    PATTERNS = client_patterns("/room_keys/version/(?P<version>[^/]+)$")
 
     def __init__(self, hs: "HomeServer"):
         super().__init__()
@@ -309,12 +335,11 @@ def __init__(self, hs: "HomeServer"):
         self.e2e_room_keys_handler = hs.get_e2e_room_keys_handler()
 
     async def on_GET(
-        self, request: SynapseRequest, version: Optional[str]
+        self, request: SynapseRequest, version: str
     ) -> Tuple[int, JsonDict]:
         """
         Retrieve the version information about a given version of the user's
-        room_keys backup.  If the version part is missing, returns info about the
-        most current backup version (if any)
+        room_keys backup.
 
         It takes out an exclusive lock on this user's room_key backups, to ensure
         clients only upload to the current backup.
@@ -339,20 +364,16 @@ async def on_GET(
         return 200, info
 
     async def on_DELETE(
-        self, request: SynapseRequest, version: Optional[str]
+        self, request: SynapseRequest, version: str
     ) -> Tuple[int, JsonDict]:
         """
         Delete the information about a given version of the user's
-        room_keys backup.  If the version part is missing, deletes the most
-        current backup version (if any). Doesn't delete the actual room data.
+        room_keys backup. Doesn't delete the actual room data.
 
         DELETE /room_keys/version/12345 HTTP/1.1
         HTTP/1.1 200 OK
         {}
         """
-        if version is None:
-            raise SynapseError(400, "No version specified to delete", Codes.NOT_FOUND)
-
         requester = await self.auth.get_user_by_req(request, allow_guest=False)
         user_id = requester.user.to_string()
 
@@ -360,7 +381,7 @@ async def on_DELETE(
         return 200, {}
 
     async def on_PUT(
-        self, request: SynapseRequest, version: Optional[str]
+        self, request: SynapseRequest, version: str
     ) -> Tuple[int, JsonDict]:
         """
         Update the information about a given version of the user's room_keys backup.
@@ -386,11 +407,6 @@ async def on_PUT(
         user_id = requester.user.to_string()
         info = parse_json_object_from_request(request)
 
-        if version is None:
-            raise SynapseError(
-                400, "No version specified to update", Codes.MISSING_PARAM
-            )
-
         await self.e2e_room_keys_handler.update_version(user_id, version, info)
         return 200, {}
 
diff --git a/synapse/rest/client/tags.py b/synapse/rest/client/tags.py
index ca638755c7ee..dde08417a407 100644
--- a/synapse/rest/client/tags.py
+++ b/synapse/rest/client/tags.py
@@ -34,7 +34,9 @@ class TagListServlet(RestServlet):
     GET /user/{user_id}/rooms/{room_id}/tags HTTP/1.1
     """
 
-    PATTERNS = client_patterns("/user/(?P<user_id>[^/]*)/rooms/(?P<room_id>[^/]*)/tags")
+    PATTERNS = client_patterns(
+        "/user/(?P<user_id>[^/]*)/rooms/(?P<room_id>[^/]*)/tags$"
+    )
 
     def __init__(self, hs: "HomeServer"):
         super().__init__()
diff --git a/tests/rest/admin/test_media.py b/tests/rest/admin/test_media.py
index aadb31ca838e..db77a45ae39f 100644
--- a/tests/rest/admin/test_media.py
+++ b/tests/rest/admin/test_media.py
@@ -213,7 +213,8 @@ def prepare(self, reactor: MemoryReactor, clock: Clock, hs: HomeServer) -> None:
         self.admin_user_tok = self.login("admin", "pass")
 
         self.filepaths = MediaFilePaths(hs.config.media.media_store_path)
-        self.url = "/_synapse/admin/v1/media/%s/delete" % self.server_name
+        self.url = "/_synapse/admin/v1/media/delete"
+        self.legacy_url = "/_synapse/admin/v1/media/%s/delete" % self.server_name
 
         # Move clock up to somewhat realistic time
         self.reactor.advance(1000000000)
@@ -332,11 +333,13 @@ def test_invalid_parameter(self) -> None:
             channel.json_body["error"],
         )
 
-    def test_delete_media_never_accessed(self) -> None:
+    @parameterized.expand([(True,), (False,)])
+    def test_delete_media_never_accessed(self, use_legacy_url: bool) -> None:
         """
         Tests that media deleted if it is older than `before_ts` and never accessed
         `last_access_ts` is `NULL` and `created_ts` < `before_ts`
         """
+        url = self.legacy_url if use_legacy_url else self.url
 
         # upload and do not access
         server_and_media_id = self._create_media()
@@ -351,7 +354,7 @@ def test_delete_media_never_accessed(self) -> None:
         now_ms = self.clock.time_msec()
         channel = self.make_request(
             "POST",
-            self.url + "?before_ts=" + str(now_ms),
+            url + "?before_ts=" + str(now_ms),
             access_token=self.admin_user_tok,
         )
         self.assertEqual(200, channel.code, msg=channel.json_body)