You could try rubbing toothpaste on an area, let it sit for a bit and then rinse it with a vinegar/water mixture and see if that gets the stains out. Bar Keeper's Friend is known to be able to get hard water stains out too. I usually keep some of that in my kitchen and use it on pots/pans. It's an acid so you'll want to rinse it very well with water afterward but it's likely to do the trick.