I use a car polishing compound to buff my headlights. It contains a very mild grit to clean up slight wear and tear on the plastic. I use the same thing to take scratches out of Compact Discs. Works like a charm. You can also use a stovetop cleaner. The ones intended for the newer smooth top units. It's esentially the same product with slightly more grit.

I have the same issue with the driver's side door. I'm waiting for warmer weather and I'll be taking the door panel off to see what's wrong.