I haven't had any trouble with .wma's. I accidentally put one on the card (my old Slvr would do EXACTLY what you are talking about, so I usually avoid windows media files) and was pleasantly surprised when I heard it play.
My fin does have a weird issue with .mp4's, tho. I make movies of the virtual reality scenarios I make at work, and love putting them on my Fin to show off to family and friends. I usually convert to 3GP with DVD Soft Free 3GP Video Converter, but I have access to Final Cut Studio 2, so I rendered a video out as an mp4 in Compressor.
My Fin is very schizophrenic when it comes to playing it

It will play it at first, then fall asleep during playback. When I unlock it, it starts playing where it left off. Then it cuts out abruptly and says unknown file type... Effing weird...
Maybe there are some settings in Compressor the Fin doesn't like?