Visible crew/equipment: In the shoot 'em up scene at the hangar near the beginning of the film, right after Tito and Wanda take down Pollux, when Troy shoots an agent in the stomach and the agent flies back - you can see at least two cable wires pulling him backwards. You can first notice the 2 wires when the agent is running in slow motion right before he shoots him. (00:14:15)
Visible crew/equipment: At the L.A. Convention Center, just before Castor Troy (as Sean Archer) disarms the bomb, there are a few shots of all the extras evacuating the area. In the interior shot, that looks out through the glass doors onto the street, the tracking crane arm with a seated camera operator and camera on its platform is visible as it shoots an exterior crane shot of all the extras, which was seen among the previous shots.
Visible crew/equipment: When Sean (as Castor Troy) is doing the 'water skiing' thing, trying to hang on to the speedboat's chain, in the close-up the harness he wears is visible under his wet white shirt. (02:06:50)
Visible crew/equipment: When Sean first visits the Walsh Institute, he, Dr. Miller and Dr. Walsh walk in front of the circular glass window to view the ear reconstruction. In the next shot facing them, the reflection of a boom operator holding the boom pole is visible on the glass in front of Dr. Miller and Sean. (00:24:50)
Continuity mistake: When Sean and Tito first drive the Hummer onto the runway, the jet is a mere short distance away, coming towards them. In the following shots, the distance between the Hummer and the jet has increased tremendously, for the ensuing drama to unfold. (00:09:40)
Continuity mistake: At the end of the film, when Nicolas Cage and John Travolta are lying next to each other in the ambulance, there is no blood on Travolta's shirt collar and suddenly, between shots, the collar is covered in blood.
Continuity mistake: On the speedboat, when the anchor comes loose from the boat's bow it takes with it a large chunk of metal and leaves a gaping hole, but next shot, as the anchor falls to the water, the huge hole is gone leaving only the bullet holes on the surface. (02:07:20)
Continuity mistake: On the chopper, when Sean Archer points his gun out the window, in the shot facing him the window to his right is a double slide type. In the next shot, from inside the chopper, his arm is through a single window that flips down. (01:23:00)
Other mistake: On his own computer, Sean looks up his son's file, which states the boy died immediately and his date of death was September 9th, 1991. When Eve and Castor (as Sean Archer) are at the cemetery, the date of death on the headstone is September 24th, 1991. (00:21:15 - 01:14:50)
Visible crew/equipment: At the Walsh Institute, after Sean gives his ring to Tito, when the stainless steel sliding door closes, the camera and a crew member, or likely the director, looking behind the camera lens is seen in the glass window reflection.
Continuity mistake: When Castor (as Sean Archer) is speared, as he stands there singing morosely his shirt is drenched in blood, but when he is next seen in the ambulance that blood on his shirt has vanished. Additionally, the cuts on his face produce blood trails which smear, when he is first speared, but in the ambulance his face is cleaned up and the blood trails are thin and neat.
Continuity mistake: When Sean (as Castor Troy) stabs Castor (as Sean Archer) in the leg, the type of speargun actually changes between shots, it is an entirely different model. The spear tip differs as well.
Continuity mistake: When Archer and Dubov are making their escape, Dubov falls over the rail and Archer catches his gun barrel then tries to save him. In the last shot before Dubov falls, Archer is holding on to the very last tip of the gun, but in the wide shot he is holding a lot more of the barrel.
Visible crew/equipment: When Sean (as Castor Troy) shoots Castor (as Sean Archer) with the speargun, when the spear is finally unloaded, in the side shot there is a thin guide wire pulling the spear tip towards Castor (as Sean). (02:09:25)
Revealing mistake: At the boat scene when Archer is holding on to the red boat and is skiing on the side, you can clearly see the waterproof boots he is wearing.
Visible crew/equipment: During the raid at Dietrich's, when Sean (as Castor Troy) hangs on to the chain then grabs hold of Pollux, in the close-up Pollux's safety wire is visible in front of him. (This is not Sean's safety wire, as seen in the following shots.) (01:39:05)
Visible crew/equipment: When Sean sees himself for the first time as Castor Troy, he takes the coat rack and slams it into the tri-fold mirror. The right side mirror is knocked back, and both the cameraman and camera are briefly visible in the reflection. (00:37:05)
Continuity mistake: After Castor Troy is told they are being followed on the runway, there is a close-up of Sean Archer and Tito in the Hummer and the rear view mirror is gone. It is back in all the other shots. (00:10:00)
Continuity mistake: When Sean Archer is flying the helicopter to keep the plane from taking off, Castor Troy shoots the helicopter windshield three times, but there are four bullet marks.
Continuity mistake: After the second speedboat explodes, when Sean (as Castor Troy) pulls the speargun trigger, Castor (as Sean Archer) grabs the spear shaft before it can unload. As he grips the gun, the problem is that in some shots the slings are still loaded, but in other shots they are not. (02:09:00)
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.
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.