When I scratched an iPod screen, here is what I learned while researching repairs. Many folks sell expensive scratch repair kits for glossy plastic screens and cases on electronics like some Apple iPods, laptops, mp3 players, cell phones, even CD and DVD. But you don't need kits. The magic ingredient is Brasso, a metal polish. An eight ounce bottle is about $3.00 at your local WalMart. Brasso is also available online. Eight ounces is a lifetime supply for polishing iPod scratches. Brasso will polish most shiny metal surfaces on these products, too.
Brasso, a metal polish that works most shiny polycarbonate plastics.
Brasso is a metal polisher. It is actually a very mild abrasive. (It is made of petroleum distillates and silica. The distillates are just the medium; the silica does the work.) It is so mild it polishes. It is designed for metal, but it works just as well on glossy, hard polycarbonate plastic, such as some iPods, first and second generation iPhone backs, cell phones, and glossy plastic laptop and electronic cases. It will work on most shiny metals, such as the metal back on iPod touch.
NOTE: This method will NOT work properly on matte finishes on plastic or metal--it can remove the scratch, but will also polish away the matte finish leaving a shiny spot. It will not work on colored or "anodized" aluminum because it will remove the color. It will not work on glass scratches.
You will also need a soft, lint-free cloth. Microfiber cloths used for cleaning LCD screens and camera lenses work well, but a corner of an old t-shirt is fine. Do not use paper of any kind; paper can be too abrasive and may add scratches!
Just put a dab of polish on the scratched area and rub with the cloth. You will have to rub a lot, and rub longer the deeper the scratch. This is by design--if Brasso were any more abrasive, it would scratch rather than polish.
Disclaimers: Before using any polishing product, be sure the polish is suitable the material to be polished and to follow directions on the label. Use this advice at your own risk. I use an iPod for our example, but models change. Newer iPods may use glass screens rather than polycarbonate plastic. iPhones and iPod Touch have a special coating that resists fingerprints; this coating may be removed by polishes. Do not drink Brasso. Never get involved in a land war in Asia.
Some people have complained that using Brasso results in fine swirl marks clouding the surface. I have not had this problem, but here are THREE RULES for best results: