There is a product called Displex which is used to polish out fine scratches from polycarbonate / plastic mobile phone screens. I used it years ago on an old nokia phone that had lots of scratches on it's plastic screen, and it made it look like new. It works also on polycarbonate cases, but be careful. If the colour goes right through the polycarbonate you don't have an issue, but if the colour is only coated over base white polycarbonate you have to take care not to place to much pressure on one spot, as the base white plastic will end showing through the coated paint colour. I haven't had any issues myself, though I've used it a lot in the past and had the practice. You can purchase it of ebay, just type in Displex.