PreseaLover

Could be that some oily residue is on your windscreen. Sometimes service stations put their glass cleaner on which is not very good and then it is made worst by them using contaminated spray bottles and dirty cloths/paper-wipes/etc...The other thing is that your wiper blades might have some oily residue from a trim/rubber restorer on it. Try using a good glass cleaner and see if it helps. If not, you find windscreen polish/compound (do not use normal compound yourself as you will scratch the glass). Once you use the windscreen polish/compound and are confident that it is all cleared up, you might want to use somethinglike Glaco (a glass coating which technically anyone with arms, a hand and half a brain can do at home but charged an arm and leg by so called "professionals" in Sri Lanka).

Also, give your wiper blades a good clean. When you say your wiper blades are good, I am assuming that they are neither falling apart nor have hardened and dried up