First eggs!

I have been impatiently waiting for the past 6 months, and yesterday finally got my very first egg from my black sex link, Patty. She is 2 days shy of 24 weeks. She even laid it in her nest box! This morning I went out and checked, and lo and behold there was another egg! Unfourtunitly it was a super thin shelled one, that had been broken. My question is, is there anything special I need to keep an eye out for, while she is adjusting to laying eggs? Her bottom seemed a little yucky this morning, and I dont know if it was because she sat on her egg that broke, and got messy or what? She also seemed to have what looked like a piece of a soft shell, still kind of hanging out of her, she was able to pass it while I was still out there, but it still worries me, she is such a sweet girl, I dont want anything to happen to her.