I just encountered a weird problem with my iPad (again) and thought I should document this for others. I performed a sync with iTunes to copy some videos over to my iPad. All went well in appearance, but after the synch was complete, the movies are all missing in the iPad Videos app.
To fix this:
I forced the iPad to check/repair files by doing a hard restart. To do a hard restart hold the iPad power switch and home button for about 10 seconds, or enough time until you see the Apple logo appear. At this point you can let go and the iPad will continue to do the restart process on its own. The restart may take a bit longer than a normal restart so be patient. Once the iPad home screen appears you can check to see if the videos are present in the Videos app. Sometimes this is all it takes for the videos to appear.
Continue with these next steps if you are still have missing videos.
Proceed to connect your iPad back to your Mac/PC and do one more synch in iTunes. I toggle a few of the main selections off/on for movies, music, podcasts. Then select the Sync button.
After the synch process completes, your movies/videos should now re-appear in in the iPad videos app. Obviously your results may vary with this work-around, but it seems to work for me whenever I run into this issue on my iPad.
Good luck and let me know if you find a better way to do this. Hopefully Apple will fix this issue soon.