During the 'SWAT' team's raid, the lead officer knocks in the door and proceeds to rush in without any weapon drawn. No professional would do this because it would leave him or her defenseless to anyone guarding the door.
For an assassin, Mr. Lucky is woefully unfamiliar with firearms. While lying in the prone position, he doesn't rest one arm on the ground to steady his weapon for his shot. He uses the wrong type of scope for the shot in question. And he doesn't remove his overcoat even though it clearly is restricting his range of movement.
When XXXX goes to lunch with the boss at the clubhouse at the beginning of the movie, the position and composition of golfers on the green and golf bags propped at the flagpole changes between the aerial and ground shot.
After XXXX places the telephone call before being abducted from his hotel room by Eddie Temple's thugs, he throws down the cell phone on the bed. In the next shot when Tammy comes out of the bathroom, the cell phone is gone.
When XXXX and Gene are drinking whiskey at Gene's flat, XXXX fills the glass closest to him first, but when the camera switches through the table, the glass closest to him is empty and he has filled up Gene's glass first.
When Tammy is undressing, she pulls off her top and is clearly not wearing a bra. Moments later, when pulling on her nylons, the bottom of a black bra can be seen at the top of the frame. This is the same bra that she puts on to finish her outfit.
Just before XXXX meets Lucky in the park, Gene beats him to a bloody pulp. But when he meets with Lucky there are no visible signs of blood or bruises. In the several scenes that follow, the blood and bruises are back.
(at around 26 mins) XXXX is dropped off by Eddie Temple. As you'll notice the car drives straight off (at around 31 mins). This not is possible as the road that XXXX lives at 7 Queens Gate Mews, Kensington is a cul-de-sac (no through road). The car would not have been able to go anywhere.
The only Police officers in London who carry or use firearms are SO19 (now CO19) or special operations (now central operations). Cody and Tiptoes appear to be drug enforcement officers so would not be present in the raid on the hide out and the 'SWAT' scene.
The scene where XXXX gives Dragan the package next to the statue in Greenwich park is incorrect: Greenwich park is surrounded by fences and shut at night between 6pm in the winter and 10pm in the summer when it is still light.
When xxxx picks the gun from the gun display at Genes apartment he picks the one on the right which is a non silenced luger. The scene where he shoots jimmy he is holding the gun that is to the right of that in the gun cabinet complete with silencer.
The pistol used to kill Jimmy is a suppressed .22LR. There's no way the police lab could match the round used to kill Jimmy (.22's are too small and their rounds usually deform upon impact) simply from the casing ejected from it. .22's are rimfire weapons and the striker markings would not necessarily be the same for each round fired. At best, they could say that the round was "consistent" with the type of round used to kill Crazy Larry, which is a far cry from saying it was from the same weapon.
Throughout the film, XXXX makes it clear that he hates guns and violence. Yet, when he hears the recording of Jimmy talking to a police officer about Gene and himself, he takes upon himself to kill Jimmy. This is irrational since it would have been easier and smarter to let Gene and Morty hear the recording and discuss how Jimmy should be silenced.
During the staged police raid, the police 'leader' in charge of the team refers to the 'Inspector Cox' initially as 'Captain', which is not a rank in any British police force. Later the Inspector refers to the leader as 'Sergeant' when his epaulettes display two bath stars, the insignia of a police Inspector.
The goof items below may give away important plot points.
The pistol featured on the movie cover is not the identical gun used during Gene's flashback. Although it's said to be the same murder weapon, both guns can be set apart when Gene opens his hidden cache of weapons. One gun has a noticeably blue handle.