When Julia Fang is locked in the bathroom, the lock and handle of the bathroom door are on the right. When the door is unlocked and she leaves, the lock and handle of the bathroom door are on the left.
Signs at a dockyard show a height clearance (for trucks)
measured in meters. Even though such a sign in the USA would have the clearance measured in feet, the scene was shot at the port in Montreal where signs would be in meters. Also the rail cars at the same dockyard are Canadian; one is clearly marked Canada and another reads "CP Rail" (Canadian Pacific Railways).
In the movie, some people speak Mandarin Chinese and some people speak Cantonese Chinese, sometimes in the same conversation. Also, Julia Fang, who is only seen speaking Cantonese, translates a poorly spoken Mandarin recording to Shaw. Also, Fang pronounces Mrs. Li's name wrong, she pronounced it "Lie" when it is pronounced "Lee". The interpreter for the conference translates the English into Cantonese, which would never be done. Most Cantonese speaking people can speak Mandarin, but almost no Mandarin speaking people can speak Cantonese.
When Shaw and Capella are in the car outside the UN building before the final scenes, Capella's Motorola i1000plus rings. While he answers it the LED on the top of the phone stays red - meaning 'no service'. He then hands the active call to Shaw who talks, and the whole time the LED is still red - the phone is not in service.
At the beginning of the movie, when Shaw uses a mirror to hookup to the laptop's infrared port, the beam coming in to the port is perfectly horizontal, which would only be possible if someone was facing the laptop and pointing a beam directly at it. Furthermore, infra-red beams are completely, 100% invisible to the human eye so the whole operation of carefully reflecting it off a mirror would be total guesswork unless Shaw has an uncanny ability to calculate angles of reflection in an object a dozen or so feet away whilst aiming for a second object that he a) cannot see and b) doesn't know the exact location of.
Although the UN Charter does not allow it to operate a counter-terrorist organization, several scenes imply that the operation is a secret initiative undertaken exclusively by Eleanor Hooks. Hooks oversees her covert team by herself, keeping the UN Secretary General (Douglas Thomas) largely in the dark: Thomas doesn't know the members of her group nor the details of what they do.
When Shaw returns Capella's sidearm outside the Chinese Club he presses the magazine eject so the magazine falls to the ground. When driving away, Shaw holds up the "last bullet" that would have been in the chamber signaling that he'd removed all the bullets from the pistol. But since he ejected the magazine from the pistol right before returning it to Capella, that would mean he'd have pulled the slide back to eject the one round while the magazine had still been in the pistol which would have just chambered another round. So Capella's pistol actually still contained a single round rendering Shaw's actions inconsequential.