Continuity mistake: While Kim is holding the baby for the first time, she has her right hand under the baby. When JD asks if he can hold the baby, her right hand has moved and is holding the baby's head.
Continuity mistake: Turk says two players are needed to finish the game. Carla later says she has finished it several times herself when playing in the middle of the night.
Factual error: The Toyota Prius uses an electronic transmission that requires the ignition to be turned on. Since J.D. said that he had no idea how to operate the car, he could not have pushed it from the parking space because he wouldn't have been able to put it in neutral.
Other mistake: Elliot told Kelso that he was getting a chocolate cake for his birthday, because she likes chocolate cake. At the party, the cut cake that everyone is eating is white. (01:42:00 - 02:04:00)
My Bad Too - S7-E7
Continuity mistake: After the kid collapses walking across the stage, J.D. and Eliot sit down in the cafeteria and start talking. J.D.'s hands are under the table. The shot switches and J.D.'s forearms are now resting on the table.
My Princess - S7-E12
Continuity mistake: Dr. Kelso already quit his position as Chief of Medicine, but he's back in the beginning of this episode.
Answer: No, it was a fake, they used a stamp.
It is real.