Joke around here is that mold is the state flower.

Plus my lot has a creek and a pond, so we have ground water just below the surface.
So far no mold issues in the run, but that's because I prioritize drainage (and I mostly provide feed inside the coop, where it stays dry and mold-free). As long as the water can flow through to the soil below (our soil inherently has good drainage) then the surface of the run litter stays fairly dry most of the time, so no mold forms.
It's a bit of experimentation... what might work great for me could be bad for you, or vice versa. Like some people happily toss fruit scraps in the run, but I don't (or I have to pick up anything left behind) because of fruit flies in the summer. But so far I've found that most leafy green plants can be safely left in there, as well as things that dry out well like the corn cobs and husks.