We haven't made the leap to a dehumidifier yet, but we do keep the heat on, and leave the kitchen window cracked. Oddly enough, the bathroom doesn't have the problem the kitchen, living room and bedroom have, despite being the one with the worst steam. Problem areas get a quick spritz with bleach from time to time.
The heat has helped us more than anything, although I am sure the dehumidifier would be better. We have to have the heat because if it is too cool, hubby's lungs hurt, so we figure we're already spending so much in gas that adding to the electric bill too is a bit much for now.
The doc can't figure out the lung thing, because he doesn't have asthma or COPD, no chronic bronchitis or anything can be found. He never had the problem in other places over here, and no problems the whole time he lived in the States. It has only developed since moving into this place, with the damp and mould problem. His doctor swears there is no connection, but it only developed last winter, which was our first winter here.