I have been amazed by the number of stories about mildewed eggs on the interwebs, about eggs that have mildewed both on the inside and outside of the shell. While I am certain that could happen if you left the eggs out for six months or a year or so, I have this to say about that–Hoya!
As a teen, I gathered upwards of a thousand eggs, literally ever day, as we had ten thousand chickens who laid hatching eggs. We were forbidden from washing the eggs by our corporate masters, as that would have affected the hatching rate. We never had a single egg with mildew, and I am guessing that I personally gathered tens of thousands of eggs.
Now that I have downsized to a flock of six happy chicks, I read a quote from a chicken prof who said that eggs taken out of a fridge and then stored in the kitchen, would mildew. Hoya! Anything will mildew if you leave it out long enough.
Just eat the eggs, the fresher the better.