I was trying to get rid of some fogginess in my driver's-side headlight and bought a wet-sanding polishing kit from Meguiar's (I recommend it, by the way). Unfortunately it didn't help much because it seems somehow there's haziness on the INSIDE of the headlight, but I decided to give the kit a whirl on my front grille and rear door badges, which had seen better days. It worked better than I expected. Here are the results: Imgur: The most awesome images on the Internet

 

I used a 3M kit on the back bumper cover on my Smart car (all plastic body) and got great results, except where I went through the clear coating. I ended up using a clear spray over that spot and it ended up working good enough. You don't notice it unless you know it is there.
I have polished a number of headlights and have been satisfied but you do have to coat them to keep them from oxidizing over time once they are done.

** great job on the badges!! **