I have removed my entire ~/.mozilla directory, purged firefox* (and manually deleted all the hanging firefox files in /etc and /usr/lib).
Possibly related: when I attempted to post this question with Firefox, the post hung, and I got an error from StackExchange about an unusually high number of requests.
Anyone else seeing anything similar? What else can I try?
It's more than just Firefox. All gecko-based applications seem to be misinterpreting keyboard input, as was Eclipse. I suspect keystrokes were going to the wrong windows, somehow.