A.  If you're certain it's mold, the simplest solution is to very lightly sand off the spots with a fine-grit sandpaper (150 will do). Remove the dust by using the hose extension from your household vacuum, or blowing it out with a hair dryer. Once you're satisfied the stains are gone, lightly wipe down the interior of the humidor with some polyglycol (50/50) humidifying solution. This will help re-moisturize the walls and help fend off any future mold spores.

You can also use a Boveda cigar humidor seasoning kit. (Note: one kit services a space for 25-50 cigars, so make sure you by enough packs to properly season the box based on its total capacity.)  Charge the humidifier, close the lid, and monitor the temp and RH in the box for a few days. When it reaches the acceptable level for you, you can start filling you cigar humidor with cigars. 

Finally, make sure you have the appropriate size humidifier and a digital hygrometer for the humidor. I suggest a bead or crystal type humidifier, which are much more stable and reliable.