Continuity mistake: When Laverne does a slam dunk, you can see that the ramp leading to the hospital main entrance has no-one standing on it or in front of it. But before and after the slam dunk you see see two doctors with a basketball on the ramp, and Franklin standing remarkably still, with a camera, in front of it.
Audio problem: Season 8, episode 7 "My New Role": Before the opening credits, JD taps a pencil against a cup, and other various devices in the hospital start making a song. At the end of this song, the Janitor can be seen playing the bongo. The rhythm of his hands do not match the rhythm of the bongo sounds at all. After the song ends, JD turns to the Janitor, who is again playing the bongo. This time, however, his rhythm of his hands do match up with the rhythm of the bongo sounds.
Continuity mistake: As JD is unwrapping the patients head while talking to the Janitor, he completely unwraps the gauze and there is 3-4 inches of hair showing. The shot changes and suddenly the head has gauze on it again and only about an inch of hair is visible above the bandage.
Other mistake: When the Janitor plays with Kelso 'double or nothing' for tossing the cotton ball a second time in the jar, Todd tells Kelso he now owes him $600, in the end it was $700. This isn't a 'double or nothing' amount of money the Janitor could generate. They started with $5, so the count would be 5 - 10 - 20 - 40 - 80 - 160 - 320 - 640 - 1280 and so on.