Definitely a trip to the vets is in order.

Depending where the spots are it could be a number of things.

I have Persians and one of them gets kitty acne which shows up at first as black spots around her lips and chin. Daily cleaning (providing the cat will let you) keeps it from infecting and spreading. Daily cleaning and topical ointment clear it up as well.

Also it could be stud tail, but like I said depends where these spots are.