Elaine's (Julia Louis-Dreyfus) vest is missing a button when Jerry (Jerry Seinfeld) first goes to the hospital, but is buttoned up again for the remainder of the scene.
During the pigman discussion in the hospital, an officer is talking to a doctor in the background; in the next shot they have vanished.
When Stan (Tom Alan Robbins) and Myra (Jeannie Elias) explain to Jerry (Jerry Seinfeld) and Elaine (Julia Louis-Dreyfus) what's expected of them regarding the Bris and refer to the baby by name. According to Jewish law, however, a baby is named at his bris after being circumcised.
At the hospital, their new-dad friend tells them that the baby is sucking away at his wife's breasts, implying that she is breastfeeding. But in the next shot, his wife's shirt is not up and the baby is not in any position to be breastfeeding.
When George is driving the gang to the hospital, his car is clearly in Park the entire time. It's not a real car, not a real road, there is not transmission. Reality TV has ruined an entire generation.
Kramer is supposed to go to Room 1397 but accidentally goes to Room 1937. He discovers the pigman and runs into the room where Jerry, Elaine, and George are. Somehow he discovers which room is the right one and makes it down six flights of stairs to get there in just a few seconds. It's not a few seconds. The break between scenes implies a time lapse. It could be a gap of 5 to 10 minutes.
Jerry (Jerry Seinfeld) does two imitations from The Godfather (1972) in Marlon Brando's voice, however the lines he quotes were spoken by Al Pacino, not Brando.