Walls:
Taking measures to reduce water leakage through the roof, leaky pipes, and the foundation (see above for each of these), as well as through the gutters (below) will go a long way in keeping the walls from collecting too much moisture.
In addition to this, make sure that the air pressure is not too high on the positive side (see Ventilation tips below). However, you do want the air pressure inside to be slightly positive.
Also, make sure that the relative humidity level is below 55% to prevent your walls from taking in too much moisture. Use dehumidifiers if necessary.