I used Flitz to polish the scratches off mine. I didn't spend a lot of time on it, but it definately made it better. I would try the toothpaste first, then look to other things of that doesn't work. Like others have said, put a screen protector on there when you're done to keep from getting other scratches.
''Life's tough, pilgrim, and it's even tougher if you're stupid.'' John Wayne