Our stuff in the (unfinished) basement got white fuzz on it last summer- some kind of mold I assume.
Running the dehumidifier uses practically as much electricity as running the AC on 80 degrees, which is cool enough for us. We keep going back and forth, but we definitely need something. Dehumidifying the upstairs is pointless as we have to have the windows open to cool it off.
We haven't seen any damage upstairs from heat and humidity, probably because there is plenty of air circulation.