A minor scratch in a window, mirror or glass coffee table may not cause any real problems, but it can drive you nuts. A major scratch or gouge deep enough to cause you to worry about getting cut on it should be professionally filled, or the glass should be replaced. But if it's small or is a moderate surface scratch that just looks bad, you can get rid of it yourself or at least smooth it out and make it less obvious.
Jeweller's rouge is a polish that jewellers use to buff and shine metal. It also smooths and diminishes the edges of scratches in glass, making them less visible. Apply jeweller's rouge to the scratch and buff it with a lambswool pad in a quick circular motion. Repeat several times until the scratch is gone. Follow up by rinsing with two oz. ammonia in two qt. water.
The very fine abrasive qualities of toothpaste can smooth out a scratch in glass. Just dab a little plain white toothpaste on your fingertip and rub it vigorously over the scratch. Wipe away the excess toothpaste with a dry rag. Repeat the process several times until the scratch fades.
For scratches too deep to buff out or smooth away, try filling them with clear nail polish. Carefully apply the polish with a nail-polish brush over the whole length of the scratch. Let it dry. Then dip a clean cloth in nail-polish remover and use it to gently work away the excess nail polish on the surface of the glass, leaving it in the scratch.