Ooooo, that's a tough one. Glass is almost as hard as diamond. I think I saw a post on here a few months ago about something used to "polish out" scratches on side windows. Maybe search this site? Maybe just replace the mirror?
Thanks for the link I've also got a scratched mirror. That looks good but not sure about removing the old mirror. Anyone have a procedure that works.Id just replace it... http://www.restorick.com/proddetail.asp?prod=ABbodymirror
Toothpaste works great on a foam pad applicator with your drill or DA sander. You can also use cerium oxide paste - that's what the pros use. Amazon has it.
Just mask with aluminum foil duct tape over top of masking tape. The aluminum foil tape stands up real well to the water and polishing action but the adhesive is super aggressive. The masking tape allows it all to release real easy.
I like this idea. Some others may work too, but I like this one best. Silica (aka "sand") is what's in toothpaste & it's quite hard. Glass is also made of silica. I haven't checked cerium oxide's hardness, but for sure you'd want something at least as hard as glass (silica) or slightly harder.
Mohs hardness scale for rocks/minerals:
http://geology.com/minerals/mohs-hardness-scale.shtml