I have cleaned many plastic crystals using the following method, you will be amazed by the results!

Before starting carefully tape round the crystal with masking tape to avoid damaging the bezel.

To remove the scratches I use a finger nail buffing stick bought from the Body Shop. It looks like a giant nail file about 1/8" thick rubber and has 3 grades of very light abrasive surface on the surfaces. Start with the roughest and when scratches removed move on to next finest and finally the very fine grade.

I then polish the crystal with "Mothers Mag" a polish used by custom car fans to polish alloy wheels to a mirror finish. This polish is paste and only a very small amount is required applied with some cotton wool. I have found paste far superior to a liquid polish which can run down the edges of the crystal.

Total time around 15 minutes.

This method just takes off enough to remove the scratches - if you use it on an Omega the engraved logo will still be there when you have finished.

Remove the tape and you have a new watch - well a new crystal!