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A good Auto Parts store may have Maguiar's Plastic Cleaner/Polish. I've used it to remove scratches from sunglasses, watch faces, etc. Using soft cotton cloth and just a little elbow grease.
http://meguiarsdirect.com/detail/MEG+G12310
http://www.autogeek.net/meguiars1017.html
First be sure the sticker goo is all gone. Vegetable oil on a soft cloth is a safe method. (Dispose of cloth safely afterwards, as it can spontaneously catch fire.)
If the plastic still looks mutilated, Novus Plastic Polish is far and away the best brand I've seen (Google for sources near you). It comes in multiple coarseness, the most coarse being used first and followed up by finer formulations. All with lots of elbow grease. The plastic will look virtually original after using Novus. Don't sweat it too much, though. The plastic will accumulate lots of scratches and dings with normal use.
The glass is really plastic and using chemicals to remove stuck on tags do smear the plastic. You may try an very fine abrasive such as jewelers rouge. Anything coarser such as tooth paste will scratch the plastic. It will be labor intensive and may not look as good as new. You could also try liquid plastic polishes available at automotive stores. I think the best and easier bet is to either replace the plastic window or just live with it.