I got my 8 little girls the last week of August and they started laying almost two weeks ago. I have been getting about 2-4 eggs everyday. Today I got 5! Ya Hoo! I check the coop several times a day for eggs. It is just so much fun! It's like Easter every day!
I really do not understand what the yucky thingys could be unless the eggs were fertile and not collected right away. Mine have always looked like regular eggs, the first ones are usually tiny and as they get bigger, some times even get double yoked eggs before they settle into their laying cycle. But then your mileage may very. I've always had a strong stomach and would not say what all I've ate and lived on a family forum.