Originally Posted by OhioYJ

Ive used 0000 and that Mothers to polish glass, the 0000 alone will clean glass. I always tend to try and err on the finer side to start with as I don't want to add scratches or marks to things. However that is pretty badly scratched in places so if you want to get all of that mark out where it was bottomed out, you will likely have to use some sandpaper, and start at 400 and work your way back up, wet sanding.

For most of that of though like those fine swirls marks were it looks like someone already tried to take steel wool to it, I think you might be surprised what some of that mothers and a rag will do. Buff that till the rag turns black, then take a clean spot of that rag to it buff it off. I bet a lot if not most of that comes off with minimal effort. For $4 and an old T-shirt, or towels you aren't out much if I'm wrong except a few minutes of your time.