I just caught one of my hens in the act of laying the egg, and I by opening the coop I accidentally scared her off.
I came back about two minutes later, and discovered one egg that had an odd white film over it. As I'm not totally sure who does most of the laying around my coop (something I'm working towards fixing), it could be that this is her first egg.
Either way, the film was pretty regular, not speckled but more of an even dusting. It washed off immediately when I rinsed the egg in water, but resisted scratching from my fingernails.
thanks in advance :)