New layers give me the occasional rubber egg or soft shelled egg. Several nights ago, there was an intact egg yolk laying on the floor under the roost.
My most memorable goofy egg layer was a home bred BSL (RIR x PBR) She had a difficult time regulating her conveyor belt. Any readers remember the Lucille Ball show where Lucy and Ethel got hired to work in a chocolate factory, wrapping those little chocolates as they came down the conveyor belt? The belt kept speeding up until poor Lucy was stuffing them in her pockets, in her bra, then she started eating them.
Well, that was my little black hen, Hola! In one 24 hour period, I watched her lay 2 rubber eggs at 5 minute intervals, followed by a normal egg the following morning.
The most common nest box glitch I find is when a hen plops a big ol' turd in the nest box along with an egg. Or the inevitable skid marks that accompany sloppy muddy days.
After the pullets get up to full production, I average less than 2 eggs/week that do not make it into egg cartons. Any dirty eggs get set aside for my own use. Any soft shelled eggs go to my egg sucking, thieving dog. Egg shells get dried and go back to the flock.
Any time I ever notice a decline in egg shell quality, I give the birds some multi vitamins. That has an almost instant beneficial effect on the structural quality of the entire egg. IMO, calcium and protein are but a very small part of egg quality and bird health.