Egg science

Taking the eggs back to the retailer sounds like a good plan to me. I am not aware of any other reason for the egg white to separate from the yoke except age, but I will circulate the question one of my listservs.

Actually I didn't buy the eggs at the farmers market but refrigerated at a store that specializes in natural, locally produced farm and meat products. I've always had good luck with this label. The eggs are never uniformly sized and are variegated in color. I did finally locate the use by date and they are guaranteed until July 29. I decided to test one for freshness this morning in a bowl of water and it lay perfectly level on the bottom without tipping upward. I'll have to ask at the market the next time I'm down there; maybe today.

I suspect as well that you've experienced a bait and switch: if they're "farm fresh" they must be, well, fresh. The only reason I can imagine for the membrane between the firm white and the yolk to separate is age. Which as we know, is a bitch.

Nothing is nicer than a fresh just-layed egg ... but with "farm fresh" at a farmers market you don't know if they have sat in a hot barn for a week before.
Get to know - and trust - the vendor(s).
Toss them out if you don't trust them to be as fresh as advertised. Be safe and avoid the bathroom.

No dates on the carton. As I said, these were farm fresh. It didn't occur to me to give the eggs the float test in advance just because I only bought them two days ago. Age could be the enemy here. Or something else.

I'm thinking in the same direction as Sarah, old eggs. Was the carton stamped with a pack date?

Another possibility would be jostling / agitation which can thin the whites (one of the reasons for not storing eggs in the refrigerator door).

You could try the old float-the-egg-in-cold-water test (sinking = good, floating = bad).

What condition is the albumen in? Is it possible that it's an old batch of eggs? I know you just bought it but...

I had that happen to me when trying to strain off the watery white. I assumed that was the reason (and that the yolk seized on me because it wasn't protected from the heat by the albumen).