I don't use GMail or Facebook, so I can't be sure there's a widespread problem, but in general the first step with Firefox problems like this is to create a new profile and see if the same problem happens there. I use the profile manager to create and select the profiles by starting Firefox from a terminal with this command:
firefox --ProfileManager
If it works there, then in your usual profile, disable add-ons or changes to default settings (in the settings, or about:config if you've set things in there too) until you find what's upsetting those websites.