After the Prius is first shot up by the helicopter, there are several large bullet holes in the hood with large areas of white surrounding them (missing paint). Later after the scene at the driving range when it is shot some more, there are now a lot of small bullet holes with smaller areas of missing paint on the hood.
When Terry visits the art gallery, he is told not to set his drink on the installation coffee table. When he looks closer to read the description card, the artist is listed as M.L. Pollard. But then Francine tells him that it is an original Habberfield Jammeson piece.
When the Captain relieves Alan of his sidearm he holds the pistol with his finger inside the trigger guard. Someone trained in the safe handling of firearms, particularly in law enforcement, would know to treat any weapon as loaded and not handle it by the trigger.
Gamble owns a red Prius. At one point, the right rear door is replaced by a gray door (due to events happening in the movie). Later, when the car is on a train, the door reverts to red. However, two scenes later, the car door is gray again.
At the beginning when Allen and Terry are sitting at their desks, Terry is playing solitaire on his computer. As the camera cuts back and forth while he shouts at Allen for his singing, the card setup changes two or three times.
When PK and Chris Danson come back from being honored by the city of New York, the medals around their neck are visible while they are boasting/talking to the other officers in the squad room. But right before they leave the squad room, the medals are no longer around their necks.
When they receive the glasses of water from the assistant the doors are actually quite a distance from the desk, yet as you see the assistant come through them with the water she is right at their chairs in the next shot when it would've taken her much longer to get to them. You can tell that no extra time had elapsed because the dialogue was continuous.
When Allen and Terry are at the McMannus Pub, there is a sing-along and a short, white-haired man is singing with the others. He is singing, then a different camera angle shows him standing in a different place, not singing; then the camera goes back to the original angle and he's singing again.
When Allen and Terry are crossing the bridge in the Prius, a Volvo semi-truck can be seen next to them on the driver's side. When the angle changes to an overhead shot, without the dialogue breaking, there is no truck there.
The shoes that Terry first wears in the ballet class scene are flat soled black sneakers. When we see him spinning around, he is wearing black split soled dance sneakers with a bendable arch. As he walks out of the class he is again wearing the flat soled black sneakers.
When arresting Ershon, Allen reaches for his cuffs revealing that his wooden gun has already been stained. Yet a few scenes later Gene informs Allen that his gun was stained by Ershon's security team after the arrest.
When Sheila was telling Terry about Allen's FaceBack app, she said it can take a person's face and tell you what the back of their head looks like. However, in the closing monologue of the film, the narrator describes how Allen's FaceBack app helped police identify someone's face by using an image of the back of their head. This is backwards from the way Sheila described it.
In the scene where Allen and Terry are at the McManus pub, drinking beer, the level of liquid rises from one shot to another. Terry also leaves the pub, even though his beer is more than three quarters full.
In the scene where Martin and Fosse are speaking to schoolchildren and get a call to collar Gamble and Hoitz, Martin is shown holstering his gun. Then the camera cuts away to the children, and Martin is shown with gun in hand again.
In the scene where Allen and Terry decide to start fresh while walking through the city without shoes, several bystanders can be seen taking pictures and videos of Mark Wahlberg and Will Farrell filming the scene.
After Hoytz and Gamble are out for a night of heavy drinking, the film then dissolves to a shot of the Sun rising over a city skyline. Although the story is set in New York City, the skyline in the shot is actually the city of Boston.
A radio call goes out for a "211 in progress." 211 is the Los Angeles Police Department's code for an armed robbery, which is derived from the California Penal Code. The NYPD code for an armed robbery is a "10-30".
At one point Allen Gamble states that this is the second time he has ever fired his weapon, but earlier on when they're at the bar drinking there are multiple still shots of him discharging a firearm in the bar. However, at the time of the bar scene, he still had the wooden gun so he must have been shooting Terry's gun, thus still being able to correctly say he'd only shot his own gun twice.
When Allen and Terry are walking up to the accountant office, Allen is not wearing his glasses. However, when they're both laying on the ground after the explosion, suddenly Allen is wearing his glasses.
As Allen and Terry are rolling around on the ground just after being knocked down by the explosion at the accounting office, you can clearly see Allen's wooden gun on the ground as Allen has his hands clasped against his head. In the next shot from a different perspective, the gun is back in the holster but Allen is still holding his head.