Whether or not the regular wear and tear has a noticable negative effect on your skiing is a little bit of a questionmark, though. I'm pretty sure Jeff was skiing on a ski that had numerous scrapes and scars when he ran 41 back in the day before anyone else did. At the same time, big, deep scrapes probably do have some sort of negative effect.

Personally i'm not too worried about the scrapes from the platform... but I keep my ski in a ski sock when it's not in use which keeps the bottom of the ski protected. A ski bag isn't necessarily as safe as a sock, however, because it's easy to get sand in the bag and then you're just sliding your ski over sand, scraping it every time in and out of the bag, not helpful.

When the ski is new you can wash the bottom with a green scrubby and some soap to remove residue that gets on there during construction, when they pop it out of the mold.

If you want to smoothen the bottom of the ski some wet sand paper (very high grit number) and a bucket of water will get you headed in the right direction. I wouldn't recommend sanding your bevels, and if you do choose to use the wet sand paper, make deliberate strokes from tip to tail, one at a time, and don't go too crazy, as you are more likely to change the dynamics of the ski in 15 minutes with some wet sand paper than the scratches you have already see on the bottom.

It will be simpler and save you headaches if you just use the rough side of a sponge or a no-scratch scouring pad.