Wow...that is strange. I would try some abrasive like Scratch Doctor. That should get it out, but I would wonder what is coming out of there. Is it coming out of the mirror or from around the rubber between the mirror and the body? Try slamming your door a bit after drying it. Maybe that would get most of the water out and you could dry it. I always open both doors when I wash my car because I always wipe down the door jambs. I close the doors a little hard to make sure all the water comes out of the mirrors.