I recently bought my son the Audio + Video version of They Might Be Giants “Here Comes Science” on iTunes. It includes a video for each song, about 40 minutes in total. When played from iTunes it’s a continuous stream; as one clip finishes the next starts automatically. I was hoping it would work the same way on the iPad, but unfortunately it doesn’t. There it stops after each clip and returns you to the main screen where you have to manually start the next. Not great for a 1 year old.
I found this blog post, which suggests that you workaround this by converting the videos into episodes of a TV season. That seems like it would work, but it’s kind of a pain since it requires you to make the change in iTunes on a computer, then sync the videos back to the iPad.
After a little more searching, I found an iPad app called Video Playlist. It’s not ideal since you have to play the videos from within it rather than the built in Videos app, but it does work. Hopefully Apple will provide native support for this at some point, but in the mean time Video Playlist does the trick.