I just spent a few days trying to fix a lock up in the video app that came with the ipad2. There are several posts around the web with the same problem, so I thought I would post my experience in the chance it can help someone.
I was watching an iTunes purchased tv series when the app just locked up. It went to black screen and I was unable access any video through the app after that. All other applications worked fine, YouTube etc.
After trying the often suggested reboot and closing the app manually several times-no joy.... :-(
What finally worked was a complete iPad reset from the iTunes screen. It's a hassle because it wipes the thing clean, but thanks to backing up to the Cloud, the only pain was setting it aside for the evening while all of my apps and files were reloaded automatically.
Glad to have it all back. I missed my icrack!
UPDATE: it happend again with the same TV episode. This time I went into Usage, then Video. I found the offending episode and deleted it. All is fine now and my other videos all seem to play.