I worked with plexiglas extesivlely for a number of years and ran my own plastics fabrication business part time for a few years. The are a number of good products on the market for cleaning Plexiglas that are mentioned here and most work well. However the most important thing before using cleaners or polishes Plexi is to wash it first with quite warm water and liquid soap to make sure there is no fine grit or dust (which is really fine grit) on the surface, especially after a road trip. Don't rub it off, sort of dab it off. If you don't, and you use the cleaner/polish you will eventually end up with a haze of very small scratches. By then it will look like a fog.
If your Plexi does have some small scratches, do the wash and then cut polish it with Brasso polish on a soft flannel cloth. You don't have to polish it hard. It will take awhile and some elbow grease but you will like the end result. The Brasso polish is suspended in a ammoma solution and will not effect the Plexi. Wash the residue off with warm soapy water and finish polishing with a clean flannel cloth and it should almost look like new. While it is still nice and clean apply a coat of the best automotive wax you can get or one of the products mentioned.
Do NOT use and cutting componds coarser than Brasso.
We used to use Brasso to finish large Plexi display objects and display cases for many types of models.
Some model buliders I know would use toothpaste for finishing off the clear canopies on their model aircraft. It has a very fine cutting compound in it also.
May your Plexiglass window live a long & happy life.
Hope this helps