It sounds somewhat like what they call feline acne. But I'm not sure about inside the mouth. The black spots do come off if scraped lightly, they are oily feeling.

http://www.fabcats.org/acneandstudtail.html

I have one that tends to get a bit of this around her chin and mouth. I wash her 'face' daily and if there happens to be an outbreak, I have used neosporin sparingly for the infected spots. Those black spots seem to sit on the skin and eventually cause sores if they are left.

The daily cleaning helps tremendously, but she has never had this inside the mouth.