When Schmidt and Jenko are in the attic of the frat house, they are holding a tablet computer with the camera feed playing. The audio from the tablet can clearly be heard from the camera feed, however the status bar at the bottom clearly shows the tablet is actually muted. This is also the same for a further scene where a smart phone is being texted on - again, you hear the clicks from the key presses but the mute icon is shown.
At least once in the movie semi-automatic pistol are shown to "click" when they run out out of ammunition, leading to one of the main characters not noticing that he took an empty pistol off a bad guy.
Semi-Automatic pistols don't click when they run dry. On the last fired round the slide would lock back, and so would the trigger, making it impossible to mistake the gun for a loaded one, let alone to pull the trigger.
While driving a football helmet golf cart onto the football field, the "faceguard" of the inflated helmet is torn off and destroyed. As soon as the bad guys exit the helmet the "faceguard" is back again.
Just after the library scene where Jenko drops down one landing at a time and then jumps over the railing, his shoes are flat-soled, instead of the cleats he should be wearing with his football uniform.
When Schmidt and Jenko are in Captain Dickson's office and he's quizzing them about his daughter, he has his gun in hand. When Jenko comes back in to the room laughing, Captain Dickson's gun is back on the desk and then he proceeds to pick up his gun again.
Schmidt has problems driving the Lamborghini, especially with shifting/using the clutch.
The Lamborghini shown doesn't have a manual gearbox, so there is no clutch to be operated.
A simple pull on two paddles behind the steering wheel changes the gears.
When showing the photo of the dealer's tattoo to the Artist in his shop, the word "BOOM" is not reversed as it would be when viewed as a reflection in a car window. The photo seems to be an enlargement of the original photo and may have been flopped horizontally when the enlargement was done.
The goof items below may give away important plot points.
After finding out that his daughter Maya is the student Schmidt had sex with, Captain Dickson sends a bunch of texts to his phone threatening to kill him. We shouldn't be able to hear when these messages arrive as his phone is shown to be on silent.
When Schmidt receives the threatening texts from Captain Dickson, his name as well as his photo is displayed with each message. This only happens when a number is saved into the phone and a photo is assigned to it. So when Maya asks him "Why does my dad have your phone number?", his covering lie about getting it from the School Directory shouldn't work as she would be wondering why Schmidt's phone doesn't just display her fathers number and a blank profile pic...
When Schmidt and Jenko go to the Psychology professor's office, the nameplate on the door says Michael P. Murphy. Later, when Deputy Chief Hardy gives the TV press conference saying that they caught the dealer, he says the name is Carl Murphy.