They say not to clean the eggs because it removes the bloom. However, if you are to clean the eggs, you should use water that's at least 20 degrees warmer than the egg because then things are less likely to permeate the membrane.
Now, being vain, and loving my colorful eggs, I don't like them to look all dirty.
So, if an egg is dirty, I wash it in plain water that is bathwater temperature. I do a quick rinse til clean. Afterwards I refrigerate it.
I'm happy because I have beautiful eggs that don't look or smell yucky.
So, this may not be the "right" thing to do, but it's what I do. So far, our eggs have tasted fine, and I'm proud to give them away to loved ones.
I figure none of our eggs last longer than a week to ten days, so I'm not overly worried about amazing longevity in my eggs.