Dehumidifer - scroll down to "Trap the Damp"
http://blog.korea.net/?p=4009You will find these in all the small to large stores. Koreans also like to use charcoal. Cheap option to dealing with humidity. Place these in the closet and around the apartment. You'll go through a lot quickly during the summer months.
MoldAvoid ground level apartments and try to get something on the 3rd or 4th floors. The location of some of these apartments are such that a lot of serious mold can grow on all your furniture, luggage, and walls. Some apartments are going to be fine, but there are cases of ground level apartments not being built right.
Black mold is dangerous as it can affect your nervous system. One teacher had a large streak of black mold next to his bed on the wall. His room always stunk because of the mold. Multiple rooms on that ground floor had issues. This was reported to the co-teachers at the public schools. The schools checked out the apartments and confirmed that the teachers had to be relocated into a different apartment building.