Your problem is most likely caused by lack of oxygen in your kiln. Firstly, the blackening spots are where the fired glaze doesn't completely cover, especially on edges of handles and rims, and the underneath clay is exposed. Because of lack of oxygen these areas are reducing and become blackened. the solution is to pack your kiln much more loosely with plenty of space around and above each pot. Even remove or loosen a bung/air inlet at the bottom of the kiln so that air/oxygen can circulate. Get back to your supplier of mugs and complain that the glazing of the pots isn't uniform.