Continuity mistake: When Schmidt and Jenko first visit 21 Jump Street and are standing outside, the doors are covered with newspapers. In the next shot when they open the doors from the inside there are no newspapers on the doors.
Continuity mistake: When Channing Tatum shoots one of the thugs in the hotel room, the thug falls on his stomach. In the next shot he's on his back and again in the next shot he is on his side.
Plot hole: In the first arrest scene Jenko (played by Channing Tatum) fails to read the suspect his Miranda Rights and the suspect is later released because of this. Miranda Rights are not read upon arrest nor do they have to be unless the arresting officer is questioning the suspect about an offense. Miranda Rights are more often read during an interview if the crime is that serious but in this instance (possession of controlled substances) the suspect would have most likely been handed over to a patrol unit with a vehicle and taken to jail without being questioned, at least by the arresting officers.