Black spots in porcelain coffee mug
This is something that can happen during the manufacture of porcelain. It is due to iron particles in the clay used to make the porcelain, they get this look after being fired. It is part of the mug itself and cannot be removed. 

Customers don't like isolated black dots on white porcelain, so high end manufacturers only sell items without these dots. But if you bought something in the mid- or low-price range, or B-ware from the high end brands, these specks are common enough. 

It is only an optical defect, the mug itself is clean and you don't have to do anything more about it.