Continuity mistake: At the office, when Sean is given the bottle of wine for a job well done, the way the bottle is held, first by the assistant and then by Sean, differs between shots. (00:20:40)
Continuity mistake: When Castor Troy opens the jet door, the wall behind the cockpit differs when he pushes Agent Winters onto the runway, and the rest of the shots. (00:11:20)
Visible crew/equipment: After Castor is captured at the airport hangar, when Sean pulls into his driveway the crew is reflected on the vehicle's surface. (00:18:15)
Continuity mistake: At the airport hangar, when Castor hits the wire gate in the turbo chamber, the top of his head is well below the metal bar. But, when the emergency shut-off is pressed, his unconscious body has sat itself up, because now the bar is at shoulder level. (00:17:50)
Continuity mistake: At Dietrich's, when the firing begins, Sasha grabs a woman and they both start running up the stairs, but a few shots later when Sasha yells, "Cas, be careful with him," she and the woman are still downstairs. (01:33:40)
Continuity mistake: In the boat scene when the white boat crashes through the police boat you can see the front of the white boat shatter and then it's okay again.
Revealing mistake: In the hall of mirrors Travolta runs behind the mirrors in order to get the drop on Cage. Cage starts shooting, but when he stops and lowers his arm the muzzle flash (and possibly the gunfire as well) from his gun continues as if he's still firing.
Continuity mistake: When Cage is rolling down the runway he appears to be controlling the direction of the aircraft by turning the yoke. An aircraft is controlled on the ground via rudder (vertical stabiliser) controlled by the feet of the pilot, and nosewheel steering, also controlled by the feet (rudder pedals) of the pilot (sometimes also with a steering wheel on the side of the cockpit). Moving the yoke simply alters the position of the ailerons, which will not steer the aircraft on the ground.
Character mistake: When Troy is getting the bomb ready, the screen shows it will blow in 216 hours, which is 9 days. Yet the agent tells Archer it will blow in 6 days.
Continuity mistake: On the speedboat at the end of the movie when Archer and Troy fly through the air, you can see foam on their clothes even though in the next scene their clothes are dry. (02:02:25)
Deliberate mistake: When they fight in the hangar and Troy is thrown back by the jet engine, his face and other parts of his body should have been burnt quite heavily. Such a jet engine has temperatures higher than 450°C about 5 meters away, and Troy is even closer than that.
Other mistake: When Troy (as Archer) goes to defuse the bomb, the #1 key lights up before he even presses it.
Continuity mistake: At the church, just as the shooting is done with, Eve is leaning down with her hands covering her head. Then, in the close-up she uncovers her head and sits upright to look around, but in the next shot, she's still leaning down covering her head. (01:54:30)
Continuity mistake: In the scene where Cage and Travolta are fighting on the dock, Cage stabs Travolta with the speargun (before he fires it). If you look at the spear after Travolta is stabbed, there is blood on it. Then in the next shot, the spear is suddenly clean.
Continuity mistake: When John Travolta is shot on the carousel at the beginning of the movie, the shot enters his back near his collarbone. When the camera moves back a second later, the bullethole is much lower.
Continuity mistake: At their home, when Sean tells Eve that he has one last assignment we see his scar. At the Walsh Institute, before the surgery, there is another close-up of the scar, but it differs from the previous shot. (00:30:20 - 00:33:05)
Continuity mistake: When John Travolta's daughter slams her bedroom door in his face, from one shot it nearly closes, but in another shot he blocks it when it's still got a long way to go. (00:54:35)
Factual error: Never mind that their faces are taken off (and a fast recovery time, as well), but John Travolta is tall with broad shoulders, Nick Cage is short and thin - how did all this get changed? I know plastic surgery is possible, but these two men would need intensive plastic surgery and would need months or years to recover, not several hours.
Other mistake: At the prison, when Sean Archer (as Castor Troy) is talking to Pollux Troy to find out where the bomb is, Pollux hands him a cigarette. Never lighting the cigarette, in the next shot the cigarette is lit and he is smoking from it.
Factual error: The premise of the film is swapping the faces of the Hero and Villain. We can see the whole face of Sean Archer is intact in a water tank, which includes his eyelids and lips. When Castor Troy wakes up and confronts the doctor, despite his face being missing, he still retains eyelids and lips, which isn't possible as they would be missing. This should result in Castor having exposed eyes and teeth. (00:46:47 - 00:48:08)
Chosen answer: Although they were on the same side, Troy is currently posing as Archer, which means he would have to do everything that the FBI would expect Archer to be doing. The whole point of the raid was to take out Archer, as well as Troy's gang. He would have rather risked killing part of his own gang than risk exposing his identity to anyone else.
Casual Person
That doesn't really make sense. In the scene, he goes out of his way to shoot him and smiles while doing so, carefully and slowly. Was not a collateral damage situation. The question is why he deliberately goes out of his way to kill him.