OP - do you use dishwasher detergent that has citrus in it? If so, that is probably what is causing the spots. We had this problem, and so did my in-laws, and it went away for both of us when we switched to dishwasher detergent that did not have citrus.
I can't remember the reason why, but something about the acid reacting with the steel. Maybe google it, this is how I found out initially.