Please allow this newby a contribution to the mystery spots thread. My tub is also a sufferer of the dreaded black spot disease. When I found this forum and realized the extent of the problem, I set out to find the best method of getting rid of these spots (Always have loved a challenge).
I have no solution to the origin of the spots, however, I have discovered an easy method for getting rid of them, once they occur. Get yourself a Mr. Clean Magic Eraser! Get the kind with the blue scrubber side and the Febreeze air freshener. This product took care of the spots easily. No additional cleaners needed. Find them in the laundry/cleaning aisle at the grocery store. You'll love these little sponges so much you won't be able to stop at the bathroom.