Ok, looked again. I have no idea what sort of bolt this is. It definately goes through to the hanger (the piece that goes into the dropout and is screwed down), and there is a nut on the back of it. I can turn the bolt, and the nut will spin. I hold onto the nut with a wrench, and while it stops turning, the bolt can still spin freely. It does not appear to back out or tighten up.

While I was looking at it, I did find a rivet that was backing out of the parallel bit. I was able to push it back into place, more or less. I suspect the derailler is simply on its way out. Hopefully I can get a few more rides in while I figure out what to do (R&R the bike or buy a new or newer one).