Every time something is broken for me on a site it is because of an addon/extension, not because of Firefox. I beleave Firefox get much blame for broken sites when it actually is an addon that the user installed which is to blame.
I even have some vague recollection of Mozilla mentioning just this. Like 99% when something is broken it not because the browser but because some addon the user installed.
So test a site that you dont think works with the "troubleshoot mode" in Firefox that inactivate addons etc to see if it works then. And if it works, then figure out which addon it is that makes the mess and to blame.