don't if it's related or not, but the plugin firefox installs isn't necessarily the newest one...so if the site you try to access requires you have the last version it'll continue to complain about that.
one way to solve this could be to do a manual install : first, remove the plugin firefox has installed.
then, go to the adobe site, and get shockwave flash player (this will point to the latest version available) in the tar.gz format
untar it with
tar xvzf install-flash-player.tar.gz
then, close firefox and run the script flash-player-installer, answer the few questions and you're done.