If the mp3 file contains special characters such as commas or ampersands, the player will give a "file not found" message. A quick look in the code shows that filenames are not escaped when given to the player.

I don't have my environment set up to make a patch, but the fix is easy enough:
mp3player.module, line 1164
$audio_url = $file;
should be
$audio_url = rawurlencode($file);