Corrosion in your voice coil gaps, tube sockets and potentiometers, and deterioration of foam speaker surrounds, would probably be the most worrisome effects of high humidity. Then there's the possibility of corrosion to any other contacts, that are not plated, in the system. A good dehumidifier, or an AC unit, should be left on at all times, except when you're listening.
tubes and moisture
I run almost all tube based gear. I live in a very moist,damp basement apartment on coastal northern California. I already use a dehumidifier every other day and cover my gear with towels after every listening session overnight and during the day while at work. Is this enough protection and what is the worst scenario here in terms of gear damage?