Pete the ex glass guy here with my two cents on this. Right about the steel wool trick. Use a #00 or #000 FINE steel wool, the finest you can get. Never wet it. Lightly go over the spots and they will come off. Just takes a bit of patience. Now, for road film and greasy smears, you know the trick, don't you? A cotton cloth, some DRY Comet or Ajax cleanser sprinkled over the windshield, and rub it.
The cleanser absorbs all the junk and the windshield will be free of any film. Go over it with something like Windex, or my favorite cleaner available at COSTCO and other places, SPRAYWAY in the blue and white aerosol can. No streaking with it. If you want to, you can use Rain-X periodically to keep the waterspotting down.
This stuff works great on the glass shower door too. Pete