hmm have you updated flash? i'm not super sure if that'll work but if it were me it'd be amongst the first places i try, especially since it seems they update the blasted thing about 1x per week sometimes.
Flash Player cannot open .mp3.
I don't think it has to do with the update status of any of the media players. Probably just one of those nuisances of the open-source browser itself that doesn't seem to cooperate with the forum software or a more general "objects" issue. I have everything updated, and I have the same symptoms, but part of it may be choice; I use blocking software extensively. [Embedded] Flash clips, for example, are allowed only if they come from youtube, but if they were posted on googleapsis.com or any other third-party server, then I take the decision per file, depending on the user who posted. If it's a bot, then you may be in for very nasty surprises, leading to infection of the computer, etc.
When you click on an .mp3 link shown in the image, firefox will ask the user what to do. If you click "Save", then the object will be saved to the place indicated in your settings (in my case "Desktop"). If you click "Open", then the default player for .mp3 files will appear (in my case that's VLan Player) that first downloads the file into cache and then opens it. Very inconvenient, of course. I guess Mozilla will get reports about it soon and issue yet another of its many updates.
Paul