Sand it with increasingly fine sandpaper (use a sanding block!) up to around 2000 grit, and then polish with 3M or Novus polishing compound. I can't remember the exact name of the polishing stuff, but I'm sure someone will.
Have you thought about just replacing the plexi? It might be a lot easier...
The simple answer : Get a new peice of plexi. That peice of plexi will never be reasonably clear again, without spending more than what it would cost for a new peice. Sanding it scratches the hell out of the surface to make it 'frosted'.
Spraying clear paint on it *might* help, though Im not quite sure. Though, if its a solvent based paint its just going to ruin the plexi.
If this were car-paint, I would tell you to get out some 1000 and 2000 grit sandpaper, and sand it smooth, then polish...
Im going to test out my theory with the clear paint, if it works/doesnt work, ill post a reply.
Edit : nope, didnt really work. It made the scratches dissapear slightly, though overall its still fairly blurry.
Flame polishing will make some improvement, but it will be far from clear. It will also leave it uneven and distorted. To work well flame polishing still requires the surface to be sanded very close to being smooth, any deep scratches from the 120 grit will most definately still be there.
flame polishing indeed helps a bit.
but the end result is far from perfect. maybe if you sand down to say 800 or 1000grit and the flame polish it will be better.
What I personally do...
Fine ( I mean VERY fine) wet sand paper, sand it down totally (take your time and use lots of water). When its all sanded I clean the surface off (soap and water), then get a blow torch out and go over it all melting the very fine sanding down to make the surface almost liquidified. If you put the torch down on a spot for to long it WILL bubble effectivly destroying that area. It also may catch on fire..
Bob hit it right on the nose. Glad you are getting a new piece. "unfrosting" or un- anything should never be done when you have a perfectly good alternative.