I just learned something that might be very helpful, but hopefully nobody will experience this.
I rented a movie from iTunes, and it was in the middle of downloading when it somebody fast forwarded to the end and said it was finished way ahead of time. Uh, I don't think so, but it insisted it downloaded and there was no means to continue. Sure enough, it only got about 5 minutes worth. Looked up how to report a problem to iTunes, and they got right on it and reset it so I could download it again. Kudos to iTunes.
Here's what they forgot to mention though. DELETE the movie before you try downloading it again! They forgot to mention that, and apparently the iPad gets really confused by that. All I got was a black screen when I clicked on videos, but after much fiddling and rebooting I finally got it to show two instances of it and I was able to delete the first instance and it behaves normally now.