Women Painters.com: Paint Issues and Fixes:

Mildew

Black, gray or brown spots or areas on the surface of paint or caulk.

image courtesy of
The Rohm and Haas Paint Quality Institute

Possible Causes:

Forms most often on areas that tend to be damp, or receive little or no direct sunlight (e.g., bathrooms, kitchens and laundry rooms).
Use of an alkyd or oil-based paint, or lower quality latex paint.
Failure to prime bare wood surface before applying the paint.
Painting over a substrate or coating on which mildew has not been removed.

Solution

Test for mildew by applying a few drops of household bleach to the area; if it is bleached away, the discolorant is probably mildew. Remove all mildew from the surface by scrubbing with a diluted household bleach solution (one part bleach, three parts water), while wearing rubber gloves and eye protection. Rinse thoroughly. To protect against mildew, use a top quality latex paint, and clean when necessary with bleach/detergent solution. Consider installing an exhaust fan in high moisture areas.