Today our IT support sat down and dug into this. The game was set to look at the course question bank but the mystery questions were pulling from a glossary in a different course (in a completely different category!). When we looked at other games we found the same problem. We went to the course and there were a couple games. We deleted the games from the course (it isn't currently in use) and all the games everywhere else started working again.
The problem is solved but we still don't know why it happened. I have a suspicion that the glossary may have been created with cut/paste from word and the creators may not have cleaned the HTML out. Sometimes the html from word is pretty ugly. The only thing I can think of is that there is something weird in the glossary html that when it got pulled into a game it freaked out the whole module. I have no idea what sort of HTML could do that but it's the only idea I have. I'm thinking of cleaning up their glossary (apparently I'm an on-line maid) but haven't gotten the chance.