I've had two problems with flash on firefox - apart from the fact that adobe is rubbish anyway:
1. On linux I installed gnash, hoping it would be a better open. A mistake: some sites refused to work with it because it does not run the latest fancy bits. I had a real job getting the linux machine to drop gnash and run adobe flash.
2. Again on linux, flash suddenly stopped working on my brother's machine (I suspect due to a faulty update of something allied to either flash or firefox). After a couple of months, him trying things ad hoc, me not having the box here to concentrate on it, we have still not got it working.
All other linux and windows boxes (about ten between us) working fine with firefox/flash. OS's are Linux Mint, Windows 2000, Windows 2003 and Windows XP.