My greenhouses are ridiculously humid (cross between a sauna and a shower), but I've only had problems with mold once, and that was on the wooden door. I sprayed/wiped it with bleach, and the problem pretty much went away.

I think I avoid mold problems by using very little wood (pvc instead) and by painting all the wood with a couple of layers of white paint.

Early on when I was trying to figure out what to grow, my tomatoes and other temperate crops did poorly in the extreme humidity, getting some type of wilt (a fungus?). But when I switched to growing tropical crops I stopped seeing such problems. Tropical plants are really good at shedding water from their leaves and dealing with extreme humidity. Plus they do better in the filtered light environment, since that's what they naturally deal with in their rainforest habitats.