I'm also using Firefox 3.6.3 with no problems. But, I believe I've experienced a similar problem in the past on facebook using firefox.
Perhaps first try with firefox addons disabled (if you have any). In Firefox 3.5.3 some people had problems with clicking in firefox under certain conditions. There is a thread about it here with a couple of possible solutions (I liked to the second page of the thread):
Someone mentioned that updating adobe acrobat fixed the problem for whatever reason. A few people mentioned that firefox add-ons were causing the problem, and several people mentioned that the problem was related to their mouse/pointer device driver. That was in an older version of firefox, but the problem description sounds similar.