Hmm, the traditional way is to start with sandpaper and work down till you're polishing with silk. I've polished heavy scrathes out of CD to the point where it'll play using toothpaste and a toothbrush, then just a toothbrush, then my fingers, but it's still quite misty to the eye at that point. I don't know how much work it would require after that to make it clear - it played well enough for my purposes at that point.
Some sort of laquer might also work, but I've less experience doing that. Might be better off doing that though if possible, as of course sanding it down removes any logos and legends from the surface, and might look a little weird if you sand around the logos and have to remove a lot.