I've always been told not to wash them if you don't need to. But lately my farm is so mucky that the eggs have been more messy than during the dry months. I only use plain water and a rag. Soke for only a short period of time if it is a caked on mess.
My personal preference is to have clean nests to reduce the need to wash. When necessary, I hold the egg under lukewarm running water and lightly buff it with a nylon net bath sponge. Allow the egg to air dry, but not in a carton (It will get stuck). Never use soap. Egg shells are porous, and can absorb the soap.
I do not wash my eggs until JUST before eating. I prefer to let the bloom do it's job until I'm ready to eat.
When I start eggs in the incubator, I won't be washing them at all.
I myself wash every egg because a chicken walks around in poop and dirt and her feet are by the egg. I wash with lots of cool water. I wash my sink out with comet amd rinse it well for cleanliness. Then lay eggs in bottom of sink letting cool water run over them and i use one of those plastic green scratcher cloths and scrub any poopy places off and rinse well then lay on towel. Egg shells have layers of shell and you can scratch a stain to leave egg. I dry each egg then put in cartons.
I don't wash until right before using them, and then only if they really need it. (Except the ones I sell, they all get washed right before selling). The eggs will last longer in the fridge if left unwashed.
eta: I do not wash ANY that I sell for hatching, only for eating.
I myself wash every egg because a chicken walks around in poop and dirt and her feet are by the egg. I wash with lots of cool water. I wash my sink out with comet amd rinse it well for cleanliness. Then lay eggs in bottom of sink letting cool water run over them and i use one of those plastic green scratcher cloths and scrub any poopy places off and rinse well then lay on towel. Egg shells have layers of shell and you can scratch a stain to leave egg. I dry each egg then put in cartons.
I have read that eggs should be washed with warm water not cool, as the cool will draw in bacteria into the porous shell as it cools and contracts.