It's hard to tell from the picture but it could be black ich, new markings on the fish as it gets older, or marks from touching or hosting corals. The black spot are usually very easy to see when a fish has it, the look like someone put pepper on the fish or small pin heads.
Check it up against the picture I attached. The one on the Top is "Black Ich" the one of the Bottom is "Black Spot" that Clowns get from hosting corals and anemones over time.
From the picture you posted it looks like it's just the black marks that a Clown gets when they start to host a coral or anemones. I wouldn't worry to much about it.
As for signs of Black ich, well outside of the black spot a lot of time there are no other signs at first, like scratching, breathing hard or flashing when a fish has ich. Usually the fish will just die from the infection unless treated or a secondary infections happens which will kill the fish very fast.
What you want to do is use Formaldehyde 37% solution, not the lower dosage they sell in most LFS. You then need to do 2 - 3 baths, this should take care of the problem.
Formaldehyde is very dangerous and you need to use gloves and eye protection. You should also use a container that you can throw away after you're done treating. Unless the fish is very expensive it maybe better to try and do some fresh water baths, for about 20-30 min each, and see if that works, than starting a treatment with Formaldehyde.