I think you are missing the MP3 decoder in MPD. You can check this by entering the following command in terminal:
mpd --version
Under the header Decoder plugins you should see the following:
Decoders plugins: [mad] mp3 mp2 [vorbis] ogg oga [oggflac] ogg oga [flac] flac [audiofile] wav au aiff aif [dsdiff] dff [dsf] dsf [faad] aac [mp4ff] m4a m4b mp4 [pcm]
If you don't see the MP3 entries, you have to manually install the libmad package. Do this by opening a terminal and entering the following command (assuming you use macports):
sudo port install libmad
Then uninstall and reinstall mpd. This worked for me.