You can use Ceriglass to polish your windshield. This product can remove light scratches also.

 

The Bon-Ami recommendation is a good one. I keep a can of the stuff on a shelf in my garage.

Using Gumout Fuel System Cleaner will also do wonders in cleaning a windshield. I saw this being demoed at a Carlisle show a few years back. I've tried it and it does a nice job.

Later,

 

I think that the smearing is on the inside of the windshield as it is posted in the Interior forum. So thinners and similar liquids are not to be used.
Could be wrong but ......
That stuff on the inside of the glass is from off gassing by the plastics etc I think.

 

OOPS! In that case, I use Hope's PERFECT GLASS cleaner. Best product I've ever found for cleaning interior window surfaces.

And I use Stoner's Invisible Glass applicator. It's triangular with a long handle. Applicator head is hinged and comes with several covers for cleaning. Secret to getting the applicator to work well is to use a paper towel placed over the applicator pad. Then using the cleaning wand, the interior surface of the window gets really clean; even in the corners and along the bottom of the windshield.

Hope this helps,