Exterior and basement doors are the ones most prone to mold, but you can discover a mold problem on virtually any door in the house. Despite the potential respiratory hazards inherent in a mold infestation, you can usually handle cleanup with gentle methods. Preventing a recurrence of the infestation may be more difficult, because it involves regulating humidity and moisture. That can be problematic in a damp basement or on a porch in wet weather, or in any interior space where there is high humidity.
Some molds are benign; some cause allergic reactions; and some are toxic enough to be carcinogenic; but they all need the same component to make them grow: moisture. Some types of mold subsist on little else, but some, such as toxic black mold, feed on the cellulose in your wall framing and your doors. If you see brown or white mold or mildew growing on a finished or painted door, and the door is otherwise in good shape, it's probably a relatively harmless surface infestation. The presence of black mold, on the other hand, is a sign that the wood isn't finished or that the finish has worn; the problem is seldom a surface one, nor is it harmless.
If you see mold or mildew growing on a finished door, you can remove it with plain soap and water, according to the recommendation of the U.S. Environmental Protection Agency. Mix a mild solution of dish soap and water -- about an ounce of soap per gallon of water -- put on a respirator and rubber gloves and wash off the mold with a sponge. It's the actual physical removal of the mold that matters; there isn't any need to kill the mold with bleach. If the mold is growing near the bottom of the door, it could be on the bottom edge, and you may have to take the door down to get all of it.
Removing black mold from an unfinished door -- or one with an old, worn finish -- usually involves extra effort. Start by spraying the affected area with enough bleach to saturate the wood, which will kill the visible mold and prevent it from turning into dust as you clean it. The Centers for Disease Control and Prevention recommend a solution consisting of one part bleach to 10 parts water. Once the mold is saturated, wash it off with soap and water. Take down the door; bring it outside and lay it flat on sawhorses if it's necessary to clean underneath it.
Once you've cleaned black mold from bare wood, you need to cover the wood with a finish to keep moisture out, or the mold will grow back. Before painting or varnishing, chip out any parts of the wood that have deteriorated with a chisel and fill the void you create with epoxy wood filler. When you finish the wood, you need to avoid leaving any part of it unsealed, so you'll probably have to take the door off so you can paint the bottom edge. Prevent mold problems in the future by running a dehumidifier or providing ventilation to keep down the humidity and moisture.