there is a product called novus plastic polish, #3 heavy duty and #2 medium duty. a glass shop might have some.
It will only work on light scratchs though, usually if you can feel the scratch with a fingernail its to deep.
#3 will really clean up a convertible or jeep plastic window, you know how they get with age.
3M makes a product called MicroMesh.. It was originally designed for the Airline industry to remove scratches from Airplane windows. Their windows are made out of acrylic (or some other clear plastic type material).
The MicroMesh System comes in a kit and looks like padded sanding paper.. The difference is the grits start at 1500 and progress up to 12000 grit.. The 12000 feels like thick paper.. It will effectively remove the scratches and give you a glass type surface..
I have used it before on some of my wood projects.. Paint it, let it dry and then start with the 1500 and progress up to the 12000.. It takes some work and time, but it is the best solution to removing scratches from any plastic type material..
Not every place handels it though.. The best way is to do a search on the internet and order it on line.. I picked mine up at WoodCraft.. A local woodworking store.. They have a web site if you are interested..It really does work...
Here is a picture and some information from the Woodcraft site..