I solved this issue by watching videos on the iPad with said iPad plugged into the wall. This keeps the battery from heating up from use, keeps it well fed, and somehow, I don't know how, keeps the Playback Error way. It works for me. It might work for you. I don't have a better solution and haven't found one yet by Googling.
That's it, with two minutes to spare!
For the previous article, see: http://jsbrookspresents.blogspot.com/2013/07/dealing-with-ipad-video-playback-errors.html