I'm not sure how I caused this to happen. Perhaps it was trying to select another character while the previous one was still moving. But the second character I tried to select, their animation got stuck and they were just twitching in place. I couldn't issue them any move orders. When I selected another character, the stuck one moved of its own volition, in a direction I hadn't told it, and the NEW character I selected became stuck. Clicking the next turn didn't help, I had to hit escape and bring up the options window, that seemed to clear it up.