Factual error: In reality, a face transplant like this couldn't work for multiple reasons. Primarily because of blood type, with Castor (Cage) being AB and Sean (Travolta) being O Negative. Organ donors and recipients need to have the same exact blood type for transplants to work, otherwise the recipient's body will reject it even with medication. In addition, intensive surgery is needed to connect a donor face to a recipient (ex. Connect blood vessels), which takes more than several hours.
Other mistake: In the scene where Archer (as Troy) escapes with Ivan Dubov we see their tracking blips still moving on the tracking monitor after their tracking boots have been removed. (01:06:35)
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.
Revealing mistake: When Cage is shooting Travolta with the Uzi type weapon in the room with mirrors, the gun has no muzzle flash in several shots.
Continuity mistake: When Troy (as Archer) arrives home for the first time, he's walking around his wife. When he says her name, his right hand is held up. From a different angle as he moves to her right, his hands are by his side. (00:52:50)
Visible crew/equipment: During the prison escape when Sean Archer (as Castor Troy) is running up the stairs towards an exit, a crew member's foot and lower pant leg can be seen in the upper right hand side. (01:12:25)
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.
Other mistake: When Archer (as Troy) and Dubov are fighting with the guards prior to Archer escaping, we see two guards looking at a computer screen which has several prisoners names registered on it, including Pollux Troy's name. Pollux has already been released from the prison by this stage, so his name should have been removed from the prison's computer system. (01:06:50)
Visible crew/equipment: When Pollux falls through the glass roof, you can see his harness pulling him back.
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.