Success polishing scratches out of plastic varies widely depending upon numerous factors. Depth of scratches is huge, deep scratches may result in removal of so much surrounding material that view through those areas is distorted. Some scratches may be so deep they must remain although appearance can be improved. In fact, polishing may result in areas of distortion spread throughout your field of view. On the other hand, if scratches are so bad that without polishing you will replace the windshield you have nothing to lose but time and effort trying to make it usable again.
Removal of scratches comes down to using abrasives in progressively finer grits until the scratches become invisible. What grit you begin with will depend upon how deep the scratch is. Deeper scratches will require that you polish a larger area around the scratch to reduce visible distortion. What you are really doing is reducing the thickness of the material surrounding the scratch to the same thickness as the scratched area. To be distortion free the entire windshield would need to be reduced to the thickness of the deepest scratch, something which is not really practical, so you work a larger surrounding area to minimize the delineation between the unworked and worked area. You might start with water and wet or dry 600 and work to 1000, then 1500, 2000 then 2500 grit, 3000 if you can find it, after which polishing compound like that use for clear coat paint might be used. Shallower scratches may be started with 1000 grit and worked upward. If there is a question start with finer grits and if they aren't removing material fast enough move to a heavier grit then back to finer as the scratch disappears and the surrounding area becomes uniform in appearance. Keeping the area being worked wet with water or soapy water will help prevent loading of the paper and lubricate the surface. You might follow that with the stuff used to repair plastic headlight lenses, toothpaste or jewelers rouge. Buffing wheels can be used when finishing but there is a possibility of leaving annoying swirl marks like those you sometimes see in paint after it has been buffed. A random orbital buffer can greatly reduce this problem, or it can be done by hand as long as repetitive strokes aren't taken over the same area.
You may find that you are satisfied before the final polishing steps are taken, it all depends upon how "clear" you want the view to be.
I suggest that if you choose to try get a piece of poly scrap to play with first.
This same method works well for polishing metals as well.
Many others will disagree, but I am not a fan of poly windshields because they will scratch, even with hard coats, although they are less susceptible. If you wear glasses, most lenses today are polycarbonate and you can get hard coated lenses in them, however eventually they will get scratches. If I were to replace a poly windshield I'd be buying a glass replacement.
Glass is more expensive, heavier and can break or chip, however it is more difficult to scratch than hardcoat poly. When you think about it glass is being used in automotive windshields to this day for a reason, it is durable. It holds up to being sandblasted at 70+ MPH for hundreds of thousands of miles and can even withstand impacts of smaller rocks without damage or with minimal damage. If auto manufacturers could use something lighter than glass they would surely be doing it in these days of searching for high gas mileage. I'm certain there is a good argument for poly as well, so it comes down to personal choice.
