My hats off to the Mark Levinson system for being able to play at least part of that disc. It is very complicated to mix MP3 and WMA on a disc and have them decoded properly for playback. That's why your computer can handle it OK.
Make an "MP3" disc, which is different than a data disc with MP3 (or WMA) files on it. Unfortunately, you cannot mix MP3 and WMA to make this disc, as the car won't have the computing power to decode it, and ID3 text (track name, artist, album) will be lost as well.
Some software allows MP3 discs to be created using WMA files, but that is because they are converting on-the-fly to MP3. Perhaps you can do this externally?
www.goldwave.exe is a great product to convert your files, if you have to do that manually.