No, I wouldn't worry. Keep it ventilated (this is always important for other reasons anyway). Should clear up as the wood dries out fully. If mold on the wood gets really bad--like, fuzzy--I would wipe it down with a rag soaked in vinegar, which will clean it and the acetic acid tends to discourage mold growth.
With respect to Batty, personally I'd be more concerned about the dangers posed to the chickens lungs by chlorine gas fumes from bleach than from a few mold spores. I live in the humid tropics and mold is pretty much impossible to avoid entirely--but this hasn't stopped us from having healthy chix for decades.