You will more than likely need a glass polish like
Autoglym Glass Polish and some 000 grade steel wool to get the job done. We also have Chrome and Glass Polish from RaceGlaze in stock which does a beautiful job. I'll have that up in the store in the next day or so. The marks are from the water drying on the glass. Doesn't have to be your wash water either, just the rain water will do that because of all the crap in the air.