There is no problem using MP4/M4V files.
/Cheers/Season 03/Cheers - Season 03 - s03e16.m4v is incorrect.
Plex is very picky with TV show naming and organization. Use what is recommended in the Plex Documentation.
Plex Documentation → Your Media → TV Show Files (Naming & Organizing)
For Cheers:
/TV Shows
../Cheers
..../Season 01
....../Cheers - s01e01.m4v
....../Cheers - s01e02 - Sam's Women.m4v <-- You can add the episode name if desired.
After you rename correctly, Plex Dance the entire show. This will clear out any incorrect metadata from the Plex Media Server database.
Also check the Agent settings in your server. Go to Settings → Agents → Shows. In TheTVDB and The Movie Database, make sure Local Media Assets (TV) is selected and at the bottom of the list. This will help prevent any faulty embedded metadata from causing issues with correct matching in Plex. If you reorder the agents, refresh the metadata for the library afterwards.
