@Ryano1432,
You can assume that the buildings were not built correctly that that the fix is expensive. Best guess is that the building got wet during construction before it was closed up, and the builder did not dry it out after closing it up. I was talking to a builder about a Red Robin getting built that got very wet on the inside, he said that it someone was going to have to bring in special dehumidifiers to dry it out before finishing the interior, which would add a week to the timeline.
I think the first thing you need to do is find out how high the humidity is, it could I suppose be something simple like the bathroom fans do not work. Given the offer to vacate the lease however I doubt it.
If you really want to stay you are probably going to have to spend a few hundred bucks on a dehumidifier, plus the electricity to run it.