Other mistake: An ambulance, when Kathy Stabler gives birth to the baby, Olivia says the baby's a girl. In the hospital, when Elliot gets to Kathy's table's room, she tells him the baby's a boy.
Suggested correction: Olivia never says the baby's a girl. Rewatch, please. In the ambulance, when Kathy is in the midst of the last few pushes to get the baby out, Olivia is watching the delivery over Kathy's shoulder, being supportive. With Kathy's last push, Olivia repeats, "Good girl, good girl," which is directed at Kathy to encourage her pushing during her delivery (timecode 00:39:20). Then, when the baby is out, Olivia excitedly exclaims, "It's a boy!"