I had exactly the same problem a couple of weeks ago (and with 4od), I deleted the .macromedia and .adobe files from my home directory but before I could check if this was the problem there was a newer version of flash out and after that was installed it was ok.
Oh yeah forgot to mention it would work ok if noscript was completely disabled, itvplayer and 4od would not play even if they where allowed by noscript (bbc iplayer was fine)
Worked fine with opera, there's been some discussion on here lately about the incompatibility of the latest flash and latest firefox.
Anyways it's working ok for me now
Just had an idea, try using "private browsing" those pesky adobe super cookies are not kept, at least it would eliminate that as the cause.