Richard, in my limited experience the biggest factor that affects mold growth for me is air circulation.
Example:
1. I sow some seeds on a pot and put a plastic cover that will keep moisture and slightly reduce sunlight, but it's a bit airtight. I usually get molds on those pots.
2. I sow some seeds in a pot and a plastic cover with some holes cut at the sides, molds usually are less likely to grow.
3. I sow some seeds in a pot and put the pot in an aquarium turned to the side, and usually these also don't get much molds.
So in my opinion as long as your greenhouse is covered and does not allow rain to get to your pots then should be okay, slightly overcast is actually nice for seed germination as well.
What I usually get is white weblike molds.
TTFN
Arvin