Cosmetic Repair

You can try using an automotive polish/swirl remover then an automotive wax. I don't know what the chemicals would do to your particular plastic, so try it out first. I have found this effective to remove faint marks from automotive paint and plastics( such as mirror housings). These have a little grit in them which will scrub down the paint a little. I used to refurbish cars/jeeps, and used this to touch up my touchup work. You can use 600-1000 grit sandpaper for more extreme 'scrubbing'. These techniques may leave 'burn' marks where you have scrubbed out the texturing of the plastic. A less extreme technique would be to just use some softened canning wax in the scratch, then polish with some 'pledge' furniture cleaner. This is the safest, and probably what I would do.

i recommend you use a product specifically designed to polish plastics. a product i've found to work very well is plasticare. it's made in englewood, colorado. i live in colo and am able to buy it at a couple of well-stocked hardware stores or from the factory. don't know about availability in other areas. if you can't find this exact product, look for another designed to clean/polish pexiglas.

The polish you can get to remove scratches from Audio CDs should work here. It is plastic afterall. Discwasher makes a CD polish and scratch remover I have used successfully on damaged CDs.

Their are plastic polishes sold at marine/boat stores that are used on fiberglass boats. I have used them on clear plastic souviner snowdomes (my wife's collection) with very good results. They polish but do not leave scratches (that I can see). Their is a bottle around here somewhere that I cannot locate, or I would mention a brand. You would want to do a test as with anything. I have never tried then on plastic that is other than clear.

DK, have you tried the boat polish on CDs? Sounds better than toothpaste which in my experience leaves discernable marks.