Don't use a paper towel!!!
There's also a product called Plexus that's for plastics, acrylic, Lexan, etc. You can generally find it at places that cater to motorcycles or boats - perhaps other places as well including online. It's not inexpensive but it's good stuff.
Another suggestion: If your windshield is really dirty, it would be best to wash it first then use a plastic cleaner to finish it up. JMHO.....
Bill