Visible crew/equipment: When Cage throws Pollux through the ceiling window, the support wire is seen in front of Cage as he's hanging from the edge.
Continuity mistake: During the runway pursuit, there is a shot from behind Castor Troy as he fires on Sean's chopper, and there are four bullet holes on the windshield. In Sean's close-up the four bullet holes change position.
Continuity mistake: While Sean tries to prevent the jet from taking off, in the exterior long shots of the aircraft there are windshield wipers over two of the cockpit's windows, but in the exterior closeups such as when Castor brings Winters into the cockpit the wipers are gone. (00:06:35 - 00:10:20)
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)
Other mistake: When Troy (as Archer) goes to defuse the bomb, the #1 key lights up before he even presses it.
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.
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.
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.
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.