Interesting. I suppose it is possible to scratch the glass with plastic if the plastic if tough enough.
To remove the marks, try a good glass polish (not the spray stuff, something like an Autoglym liquid paste type stuff). Will remove any Rain X or suchlike, but should bring the glass back to original condition.
Personally, I would use de-icer to clear the window, or a luke warm water then put the wipers on fast so it doesn't freeze again. Got to be careful not to crack the window.
I was watching QVC tonight and some guy was showing a demo of pre-deicer. You put the stuff on your window before it freezes and it means a quick use of the wipers and it's clear......but the windscreen looks smeary as heck. I reckon this stuff is a thick oil/gel so I don't know whats better-frozen window you can clean or a smeary mess.
I know which one I would go for.
Steve - 2002 1.4SE petrol, Silver, black/black interior, Then an identical replacement 2003 A2. Now a Toyota Corolla 1.6 T-Spirit