In this episode, like many others, a woman has to give birth in the ER under emergency circumstances. While dramatically compelling, that simply doesn't happen in real life, because ALL cases involving pregnancy complications are immediately sent to the OB-GYN units. The OB resident would either have not asked Mark if he could handle Jodi O'Brien's pregnancy herself, or Mark would have said no to his request and taken her up there himself as soon as she showed clear problems.
Dr Greene asks for 0 neg blood for a patient that had been cross matched hours ago, it is unlikely that er would waste universal donor blood unnecessarily.
When checking the progression of labor for Mrs. O'Brien both Dr. Green and Dr. Carter used regular gloves and not the required sterile gloves. Not using sterile gloves leaves the infant and mother both at high risk of contracting any number of severe infections that the doctors carry around on them throughout the day.