At first I assumed it was my fault, but by a process of slow elimination I tracked the problem down to the Firebug add-in. This is Firefox's debugger, and pretty well indispensable, so I had to get it working again. I won't bore readers any more with descriptions of all the dead ends I went down, but here for posterity is the fix.
I had to create a new Firefox profile (by default you have called 'default'). From the command line, type:
firefox -profilemanagerThis brings up a simple dialog that lets you create a new profile. Of course, Firefox now looks like you've just installed it for the first time, so you have to restore any settings you want, and reinstall your add-ins. However, it fixed my problem, and Firefox/Firebug now appear blisteringly fast (I believe the program had been silting up for quite a while). It also got rid of the many incomprehensible warning messages that Firebug had been sticking into the console log since I upgraded to Firefox 4.