When the Janitor first shows JD the penny he stuck in the door, the way he is holding it changes from bottom to top repeatedly as the camera angles change.
When J.D. presents Dr. Cox a book with all of his rants over the years, Cox asks where he can find a particular one. J.D. points him to the glossary, which tells Cox which page to go to. That would be in the index, not the glossary.
JD shows Dr. Cox that the page he wants in the book of rants is 19, but when Dr. Cox is shown holding the open book and supposedly looking at page 19, he is obviously much farther into the book than page 19 (more like page 100).
When the Janitor shows JD the penny he got stuck in the door, it shows the penny being made in 2006. JD would have gotten the penny stuck in the door in 2001 when the show aired and the penny from 2006 couldn't have existed. (This might be on purpose because the Janitor is known to lie a lot.)