The proximate cause was iTunes and an effort to fix a problem with videos in iOS that I have encountered before and which reliably enrages me. Basically, if you buy a video in the store and try to download it, but fail in a particular way, the iPad doesn't have it, but you have sort of a placeholder that cannot be deleted. Things have improved in that you can now delete the entire associated season and recover that way, but before (or if you want to delete just the one item) you have to do a sync and remove it on the laptop/desktop side.
Alas, there had been so much activity that the sync wanted to catch up on, that the sync got into a horrible state. I wound up having to delete a ton of stuff because it got screwed up (most obviously with mismatched or missing thumbnails, sure to make my son go bonkers). If only I had just deleted the one season and redownloaded it, right?
Anyway. I didn't attempt to redownload everything I deleted, but picked and chose and added a few new Xmas videos from her favorite shows. By the time she got back, I had mostly settled down and the downloads were done, so that's better.
And I'm never, ever, ever going to sync that iPad ever again. R. says they might want Oren R. music, which we only have on CD; that could cause a future problem, but I'm not dealing with it right now.