Continuity mistake: After the incident with Karl, when Castor (as Sean Archer) and Jamie are in the living room, he opens the cigarette case and offers her one. The way he holds the case noticeably differs between shots.
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: 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.
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: 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.
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: In the shoot-out sequence in the Mexican Standoff scene between Archer, Castor, Sasha, Eve, and Castor's two bodyguards, you don't need to look carefully to see that the exact same footage is used twice at different times to show a flowerpot exploding. Also, a bad guy gets shot and falls the exact same way twice at different times. He doesn't even fall at a different camera or body angle.
Continuity mistake: When Castor Troy first arrives at the airplane you see another business jet in the back (you see the red engine coverages). Few seconds later there is a different aircraft with a propeller and no jet anymore.
Continuity mistake: Towards the end of the boat chase, the "Coast Guard" boat is facing towards the two boats. A few seconds later one of the chase boats flies through the Coast Guard boat from its rear. It would have taken too much time to spin that boat around for the boat to crash through the back. And even if it were possible, most of the crew were shot and fell off the boat. Who drove the boat to position it for the crash?
Continuity mistake: Castor Troy puts three bullet holes in the windscreen of the helicopter Sean Archer is in at the start of the movie. When Archer moves toward the hangar to shoot Castor, you can see in the background that there are now no holes.
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.