My understanding is that the majority of the case is clear anodized aluminum. A few parts, such as the strip below the keys, appear to be silver painted plastic. IIRC, anodized aluminum is an oxide coating electrically applied to the metal. It tends to be pretty hard, but somewhat brittle - if you bend the metal, you see the coating crack and distort. The anodize can be chipped or scratched, and chemically dissolved, probably either with acid or alkali. Some users report palmrest marks, and conjecture it's acidic body fluids. IIRC, hobbyists remove anodizing in caustic solutions. Maglites are anodized. I do not think abrasive polishes with help, but make it worse.
IMO, I think the only thing to do is use some liquid cleaners on a cotton rag. I use Windex, Formula 409, and sometimes alcohol. These should have no effect on anodizing. Keep alcohols away from the plastics. If you are lucky, dark smudges are only dirt and can be removed. I suppose it is possible that the anodize is corroded, and then you can only replace the case to restore the appearance.
The markings seem to only be a form of paint and once scratched off, are gone forever. On my screen, I use a very clean, barely damp with kitchen detergent solution sponge, then the barely damp sponge with water only.