During occupancy, watch for visible signs of mold growth and musky odors, signs of moisture damage or discoloration, and locate the source. On a regular basis:

Make sure drain pans are working properly.
Follow the HVAC maintenance schedule.
Verify that air filters are changed and scheduled for cleaning.
Watch for leaky pipes and repair them immediately.
Watch out for sprinklers that may be aimed at the building, and check for any accumulation of rainwater near the foundation and on the roof.
Check for unsanitary conditions and odors.