Mold growth is always caused by too much water or humidity inside the living spaces. Reasons for high humidity: water leaks, no or low performing exhaust fans..
Old doors and frames painted before 1980 usually have lead-based paint. When the door rubs against the frame this will create dust. This area is called a friction point and can be found on windows as well. Lead dust is dangerous to children under 7.
Proper mold remediation is done by trained workers appropriately clothed with mask. Correctly installed and functioning engineering controls. Ducting is well sealed. Descent electrical wiring for machinery along with correctly installed lights.