I usually just wipe mine off with a damp sponge if they are dirty. If they are really a mess then I actually wet the egg itself and use the sponge. I then allow them to dry completly before putting them in cartons.
My girls always make a mess with their dirty feet since they free range a lot. They can be pretty gross at times!
We rarely get a dirty egg. If an egg needs to get washed, I just put it in the carton to be used next, rather than in the usual spot in the rotation. It goes in front of the oldest eggs, not in back of the freshest eggs. That way, I'm not storing an egg without the bloom.