Many people have asked me over the years what they can do to remove or minimize scratches on metal surfaces. There are cleaners and polishers you can buy, but before you do, try something you already have - Toothpaste. This is something I've done for worn faucets and shower fixtures to bring that shine back.
As always, try on a small less visible area first. Use a soft sponge or a old toothbrush and apply toothpaste and brush the area in a circular motion as if you are cleaning your teeth. The toothpaste acts like a fine abrasive that can remove grime and polish at the same time. The finish will not be as professional as a buffing machine or Dremal tool, but it can help smooth out a scratch or polish up a old faucet.