I'm not sure what you mean by black specs. As in colour or as in little pimples? If it's like little pimples, it could be acne.
If you are using plastic bowls and/or a plastic placemat then it very well could be acne. Plastic gets scratched and harbours bacteria.
If you are using plastic, try changing to stainless steel dishes or glass dishes (ceramic can also get minute cracks in the glaze and harbour bacteria). Don't use the same dish twice without washing it out well first. I bought about 10 SS bowls at the dollar store and they go into the dishwasher to be cleaned and sanitized after each meal.
You could dilute some hydrogen peroxide (undiluted it burns tissue at the injury site), clean his chin and mouth area with that and it should clear up the problem.
If it's just a colouration issue, then I don't know what to tell you except to have it checked out by a vet to find out why it would start to discolour.