Thanks very much for your reply. Yes, I have sand and pea gravel in the run on the ground for drainage and it appears to be working well. We just have been getting pounded by storms at about 4PM and again overnight for the past week so it is not getting the time to dry out properly. Better than it would be though if the run was just dirt, for sure! The house where they spend the night has a closed front (two latching doors make up the front). The sides each have a 24" sq window. The window on the exterior of the run/coop gets closed because it is exposed to the outside, unprotected area, but the other window which is in the protected area is left open for ventilation. During the day both windows are open and the lid to the nesting area gets propped open as well and I have been setting up an oscillating fan in there during the daytime to help dry it out. By the time it is bedtime for the ducks, everything is completely dry. Then when I let them out in the morning and I inspect the house I have found blue/green mold growth already forming on their droppings. Distressing! Anyway, I ended up removing all pine shavings yesterday and disinfecting the whole thing, letting it dry for a few hours, and then added new shavings. I am hoping this solved the issue. I know the key to keeping it at bay is to keep it as dry as possible.
As far as the coop design goes, we do have rats and raccoons here, so the open house is not as feasible for us. I will add windows on the front doors though and cover the openings with hardware cloth. That may help a bit.
Anyway, thanks so much for your input. I so much appreciate it!