When Eric is telling Jenko that he doesn't trust him because he looks 40. He says, "After a stunt like that, there is no way you can be cops," and although his mouth is covered you can see that it is not moving at all.
When Schmidt (Jonah Hill) is praying to Korean Jesus the figure has a dove in his right palm which is held out. In another scene later in the movie you see Korean Jesus again but minus the dove in hand.
(at around 1 min) When Schmidt and Jenko first open the door for their party there are 3 guys at the door (Zack, Roman and Delroy). When they show them walking in Delroy is not shown walking through the door.
When Schmidt tells Jenko it might have been a bad idea to put a wiretap on Eric's phone, a substantial number of cops can be seen behind Schmidt. The camera cuts to Jenko and then back to Schmidt where a lot fewer cops are seen behind him. The camera cuts back to Jenko and back to Schmidt one more time, but this time there are no cops anywhere. The number of cops behind Jenko doesn't seem to change, however.
When Schmidt and Jenko walk through the church doors at the 21 Jump Street Church there is old news print covering the doors. During the next shot when they're walking through the doors the newsprint is missing.
When first arriving at the school and analyzing different groups of kids, an Asian girl with spiked hair can be scene wearing a Panda dress. Shortly after as Schmidt and Jenko talk with Eric by the cars, a different Asian girl is now wearing the Panda dress.
When Jenko is writing on the board in AP Chemistry after he is taken the drugs, the sound and image reveals he is writing with a piece of chalk. When camera changes angles it is shown that he was in fact writing on a white board with marker.
(at around 1h 13 mins) During the motorcycle chase you clearly see that the traffic has been stopped on the highway to shoot the scene. This takes place when Schmidt and Jenko are seen on close up and through the rear window you can see a car across the street.
Much of the Korean writing seen in the church is grammatically incorrect (and the same Korean translation found on online translators). For instance, the Korean version of "Aroma of Christ Church" is written in a manner where Christ Church is possessive of the word aroma, e.g., "Christ Church's Aroma" or "The Aroma that Belongs to Christ Church").
Towards the end of the movie when Jenko attempts to shoot Mr. Walters, Jenko pulls the trigger on his Glock pistol twice. If a Glock is empty of ammo, you can only pull the trigger once and it will stay in a locked position.
During the motorcycle chase scene, one of the gang members shoots a gun with his right hand while appearing to accelerate. This is impossible on this motorcycle, as the throttle control is on the right handlebar.