Nothing beats a good inspector. But it can be difficult to find one, and depending on the situation you are in (apartment, condo, house, etc) it can be hard to do an inspection thoroughly. The best thing to do is to rule out causes of moisture intrusion. But even that can be misleading because previous owners may have had a leak and fixed it. If you are lucky (or unlucky) they may have left trace of the water damage so you can get an idea if it was repaired correctly. But sometimes these things are fixed leaving no trace of the water damage, but without proper containment/cleanup and then you get mold dust and toxins spread throughout the area that can still make you sick after the water damage itself is fixed. Its really a very tough problem to solve.
If you live in an area with high humidity, running a dehumidifier (or two - depending on the design of the house) is a necessity. They say keeping it below 60% is OK, but if you buy a dehumidifier I'd just set it to something really low like 40% - especially if its in a basement. Better safe than sorry.