Are you sure it's mold? Cigar mold is usually bluish-white and looks "hairy". Other forms of mold might look like you describe. See instructions for treating the beads and humidor, below.
Could it instead be tiny flakes of tobacco from years of storing cigars in there? If so, no sweat. Rinse them off and allow to partially dry, they'll be fine.
Or could you be seeing eggs or fecal matter from (dreaded even more than mold) tobacco beetles? Or even tobacco "dust" from a beetle infestation? If beetles or larvae are involved, inspect every cigar in that humidor immediately, then bag 'em in a ziplock freezer bag, remove as much air as possible, and freeze them (zero degrees Fahrenheit or colder) overnight to kill the critters. Let them return to room temperature gradually while still sealed in the bag; transferring to a refrigerator as an intermediate stage might not be a bad idea.
While the cigars are going through the freezer treatment, rinse the beads and perhaps pop them in a low (150 degrees F sounds about right) oven long enough to kill any mold or beetle eggs, vacuum out every last trace of black specks in the humidor, maybe even gently wipe the interior (especially the corners, poke cloth in with a toothpick) with vodka; the alcohol should provide a degree of disinfection. You may need to re-season the humidor after the vodka evaporates, and of course you'll have to rehydrate the beads after they cool. Or if it's a relatively inexpensive humidor, either toss it out or give it to the kids (after cleaning) as a pretty box for storing small non-edible items such as crayons or Green Army Men.