During the hangar shootout one of Archer's federal agents is killed with a shotgun blast (we get a good look at his face), yet a few moments later you notice the same agent is standing, alive and well.
(at around 12 mins) During the airplane scene the #1 engine is shot out but the fire warning in the cockpit shows #3 engine.
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.
(at around 2 mins) When Sean Archer is shot while riding the merry-go-round with his son, the bullet hole appears to move. At first it is high up on his back, and in the next scene it is further down.
When Castor Troy is captured at the beginning of the movie, he is clearly in possession of his famous twin 1911 gold-plated gun, yet later, when Archer goes to Dietrich's apartment, Dietrich gives him the same guns.
(at around 37 mins) After the face surgery, Archer (as Troy) says his voice still sounds the same. Dr. Walsh tells Archer that he's implanted a micro-chip on his larynx, so he'll have to be careful because pressure, a sharp blow, even a violent sneeze would dislodge it. If this was the case, the micro-chip would have easily been dislodged in first prison brawl between Dubov and him (at around 42 mins).
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.
(at around 1h 35 mins) Near the end of the raid on Dietrich's place, Loomis busts in armed with a , with an underslung M203 Grenade Launcher. He fires the launcher twice in rapid succession. The M203 is a one-shot launcher and requires reloading between shots. There is no indication that Loomis bothered to reload at all.
In the hangar scene when Castor and Archer point their guns at each other, if Castor's gun was really empty the slide would be locked back.
(at around 1h 50 mins) In the funeral scene, the flag draping the casket is lying in an incorrect orientation. It is conventional for the union of a United States flag to be at the head and on the left side of the body, covering the heart.
(at around 40 mins) The Geneva Convention regulates the treatment of victims and prisoners of war, not criminal prisoners of society. The guard makes a reference to the Geneva Convention simply to intimidate new prisoners and give the impression that the prison guards are not limited to any domestic and international laws that protect mistreatment of prisoners.
Only Dr. Walsh, Dr. Miller, and Tito were set on fire in the lab. Dr. Walsh knew Sean and Castor by name and by their face, the other assistants who helped during surgery weren't told anything about Sean's mission.
At around 1:38:00 Castor (as Archer) says "I don't know what I hate
wearing worse: your face or your body." but they only swapped faces. They also adjusted the rest of the body to match the other persons measurements. This whole process is explained by Dr. Walsh the first time Archer meets him and sees Troy still living.
Archer's wife doesn't notice her husband's body is entirely different when they make love. Also the film doesn't explain the change in eye color, teeth and height. When Archer visits the Walsh Institute, Dr. Walsh explains every step of the process. Archers body will be adjusted in every aspect to match Troys. This will later happen with Troys body to match Archers figure in every detail.
(at around 1h 55 mins) In the shootout at the church, Sasha didn't realize that "Sean" is actually Castor when his gun was pointed at "his own wife" and his henchmen are not pointing their guns at him but at "Castor, " because she was more focused on preventing from Castor from getting killed as she promised she would.
(at around 2h) Obvious stunt doubles during the boating scene.
(at around 14 mins) In the warehouse shoot-out in the beginning, the stunt cord is visible as the officer who is shot with the shotgun is blown back.
(at around 46 mins) When Castor awakes from coma, he starts taking off the bandage. He's not supposed to have skin on his face, but in one shot, he still has it on forehead and on the left side of his face.
When Castor is pushed into the blowing heat from the plane engine by Sean and is thrown back, the man that lands against the grill is so obviously the stunt double; he has a different hair cut than Castor and really doesn't look anything like him.
(at around 1h 2 mins) When Troy (as Archer) enters the code to defuse his own bomb, the #1 on the keypad lights up before his finger touches it.
(at around 1h 45 mins) In Troy's blood test results the word "hematocrit" (or "haematocrit") is misspelled as "hemotocrit". Besides, some numbers (such as the white blood cell count or its reference range) are clearly made up.
As Dubov is dangling from the hand rail, holding on to the but of his rifle, Archer grabs the barrel to keep him from falling. Though his hand is slipping, his grip is somehow strong enough to (temporarily) hold the weight of a man of certainly 200 pounds by a small diameter barrel with a smooth surface, with a single hand.
Approximately 7000 bullets were fired from one 20-25 round magazine that was never once refilled during the boat chase.
(at around 1h 24 mins) When Jamie is being smooched by her date, she says, "Karl, stop it!" but her lips do not move.
(at around 2h) When Castor as Archer hops into the speedboat after killing the owner, Archer fires his weapon at Castor, but the shot is heard significantly before he has fired.
(at around 14 mins) Near the beginning of the film, when Castor Troy turns round and sees his brother Pollux Troy being pinned down by cops, the camera zooms in on Pollux's face as he shouts "CAS!". However judging by the lip movement and expression of Pollux, it's obvious that the word was dubbed over the video.
In the shootemup scene at the hangar, at the beginning of the film, Castor Troy shoots an agent in the stomach and the agent flies back - you can see the wire pulling him backwards.
(at around 1h 30 mins) When the swat team begins shooting into Dietrich Hassler's apartment, Archer grabs Sasha and her son, and jump behind the bed. Dietrich is then seen sitting on a couch, as Dietrich stands and begins to walk, a camera can clearly be seen rising behind and to the left of him.
(at around 1h 1 min) Immediately after the motorcycle cop pulls up during the Convention Center evacuation montage there is a wide shot of the frenzied street; in the background a camera crane with camera and operators is visible as it tracks upward.
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.
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.
(at around 53 mins) The choking that Archer gave Troy during the visitation scene should have been more than enough to dislodge the microchip in his larynx, therefore preventing him from talking in Archer's voice for the remainder of the film.
(at around 1h 35 mins) During the raid on Dietrich's apartment, Archer (as Castor) grabs a FBI SWAT member and says "Buzz" as he remembers him, however at that exact point, Dietrich is seen behind Archer's right shoulder. Archer makes out that he "killed" the SWAT member, but Dietrich saw Archer compromise his cover and then fire one round into the floor.
When Castor sets the bomb it is set for 236 hours (just about 10 days) after the initial surgery, there is a shot of the bomb indicating it was about 216 hours. There is no way that the surgery and subsequent healing process, in addition to the chase, capture, interrogation, etc. that took place in such a short interim.
After Castor Troy becomes Sean Archer, several times throughout the movie he is seen walking about with two of his henchmen - a bit dangerous if anyone saw him with them?
While it is possible for someone with type O blood to donate to anyone, they can only receive type O blood or tissue. Similarly, anyone with type AB blood can receive from anyone, but can only donate to type AB. Sean's blood type was O, Castor's was AB. Thus, While Castor could take Sean's face without rejection, Sean could not do the same.
(at around 25 mins) Reflected in the window as the ear is being reconstructed.
Several times during the boat chase Archer still speaks in Castor's voice despite dislodging the microchip in his throat earlier.
Troy-as-Archer prepares a romantic dinner, including twin lobsters. Later, it is revealed his wife is a vegetarian. She should have realized that something was wrong when he served her meat (seafood).
Sean is only a few feet away from the boat house when it blows up yet he walks away basically unscathed.
When Castor sees his brother dead he rubs his face with his gun but doesn't react to the heat that was generated from shooting at Sean just minutes before.
(at around 1h 2 mins) After Castor (as Sean) defuses the bomb, the display shows two seconds remaining. The news reporter states that he defused the bomb with one second remaining to create suspense, significance, and to portray Sean as an even greater hero.