This has been a problem with TV Shows home sharing on iOS devices for a long time, and I've been dealing with it for a while all the way up to my current iPad3.(my Apple TV always had NO problems) Most of the many articles written tell you to fully populate meta data for imported videos with artist, season, episode, etc and not having duplicates in the same show, etc. This is a pain if you have a bunch of random videos and have to keep making up this fake data just to get it to work.
So when I upgraded to iTunes 11, all of a sudden the problem seemed to go away, and artwork was correct for all TV shows, no missing/duplicate artwork or inaccessible shows, and the individual episodes finally had different art, not identical for each episode in the show as it had been before.
But then *something* happened and it got all messed up again, I think when adding new TV Show content. The TV shows got all messed up again, and a new strange thing happened, the disease spread to Video Podcasts as well. This is a new problem in iTunes 11 that I hadn't seen before. Luckily, Movies and Music Videos are still unaffected by the problem, that would be catastrophic.
I was able to get it back working again by deleting all TV shows and re-adding them, but this is not practical as I have thousands of videos in TV shows and this takes a long time.(in addition to my iTunes holding thousands of movies and thousands of music videos, which so far have been unaffected by this disease)
I don't think this problem is over yet...unless I'm missing something.