If the moisture is caused by steam, then your best bet to control moisture is to install an exhaust fan matched to the size of the room, vented to an outside wall of the building. Only by removing the moisture from the room will you prevent it from breeding mold. But if the mold is occurring in the bath or shower at specific places, such as the joints between the tile and the bath or shower floor, then the problem might be more than steam--it might be water getting behind old grout or caulk and into the wall. You might need to strip out the old grout or caulk and replace it. Caulk, in particular, lasts only about 5 years before needing replacement. Remember that the old stuff needs to be removed before you can replace it, and that you'll need a product designed for baths. For walls and a general moisture or humidity problem, you can look into one of the mold-resistant bath paints. I haven't tried them, and all latex paints have some mold resistance, but it can't hurt. A weak dilution of household bleach in water, used in a spray bottle and paper-towelled off, will kill mold instantly, but your goal is probably to avoid having to do that and the exhaust fan is an excellent investment, IMO.
