Plastic polish

In the UK a Leicestershire firm make a plastic polish called Greygates. It's meant to be used to clean acrylic sheets. The cheap and easy way is to use toothpaste. smokers (powdered) toothpaste is also effective. Either type will get rid of shallow scratches in plastic and are especially good on clear plastic to give it a sheen.
Just dampen a bit of old T shirt, wrap around your finger, dip into the paste and use circular motions on your surface. Wash off with water occasionally to check the results.
Pete

Marty,
There are lots of different options for polishing plastic.
Firstly, you have to get rid of the sanding scratches by using progressively finer grades of sandpaper - once you get rid of the larger scratches and get down to 1500 or 2000 wet or dry, then it's easy to polish plastic.
Brasso works very well, I use Meguiars yellow wax automotive polish on plastic, plastic supply outlets (for perspex and stuff like that) will be able to sell a polish designed for perspex - motorcycle shops sell (or they used to) polish for helmet visors -
I've never used toothpaste before - I hear it works ok. Also give your models a fresh, minty fragrance.............
Cheers,
LeeTree

Novus makes a polish in (their) #1 #2 or #3 . Number 1 is finest polish, 2 more corse etc. After the 2000 grit sandpaper Novus2, then buffing with Novus 1. You can usually find it in hobby stores or Micro-mark has it. Polish (above posts) would work too (after 2K sanding), anything you can get in quart or gallon will be cheaper. Happy buffing.........
G.L.