The Mac extensions should show. On OSX Finder->Preferences there is an option to always show extensions, but this doesn't affect the naming of my downloads, only the files I create. If you are using OS9 or earlier, the names might be getting truncated and you'll have to edit them to manually add the .mp3 extension. This sounds doubtful (test by downloading a short name mp3) and once it shows "complete", check your shared folder to see what name it ended up with.

If all this doesn't work, uninstalling (along with the preference files) and a new clean install would be next.

Cheers