Go ahead and rinse the mud and poop off the eggs. Duck eggs are more water-proof than chicken eggs and it won't hurt the eggs. You will have a better hatch if you spritz the eggs every day with water that is the same exact temperature as the inside of the incubator. The easiest way to do that is to keep your spray bottle of water inside the incubator.
Duck eggs get a "cool down" every day, so don't worry about having the incubator open to spray the eggs or to turn them, They are supposed to do better on their sides and hand turned. (I haven't used an automatic turner to compare.)
I suggest that you candle the eggs before they go into the incubator. If you find any cracks, seal them before you put the eggs into the incubator. The cracked eggs might not hatch, but give them a chance.
