Make sure the file name isn't too long -- Mac's only use 32 characters, so I shortened all the song titles. Then add .mp3 at the end of the file.

To change the file name -- double click the folder that holds your MP3's. Click 1 time on the file name -- not the icon. It should change color. Start typing the new name, remembering to add .mp3 at the end.

Open Quicktime (or whatever MP3 player you use.) Go to FILE, Open Movie, and from the window that appears go to where the file is stored and double click it. It should then play.

The above solved all my Mac MP3 problems and this solution is listed in the Mac FAQ posted by LimeWire (see first post by moderator).