If anyone else has had trouble adding videos under the "TV Shows" tab, I've found a work-around. (I file my Broadway and early TV videos as TV shows, with the different chapter stops as "episodes.")
You can't add a new "TV Show" the was you can simply add new music or new single-file movies. If you do, iTunes will delete or hide all or some of your previous "TV Shows" on your device (I watch them on my iPad) or make crazy duplicates of them.
But if you add the new material to iTunes (as a Movie), change it in Get Info to TV Show, set the artwork and THEN move the ENTIRE TV Show collection to your device--as if for the first time--it works,
The move takes a long time, because video files that are an hour or 2 hours long are very large, but every other shorter workaround seems to make iTunes explode.