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: 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)
Character mistake: When Troy is getting the bomb ready, the screen shows it will blow in 216 hours, which is 9 days. Yet the agent tells Archer it will blow in 6 days.
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.
Factual error: Never mind that their faces are taken off (and a fast recovery time, as well), but John Travolta is tall with broad shoulders, Nick Cage is short and thin - how did all this get changed? I know plastic surgery is possible, but these two men would need intensive plastic surgery and would need months or years to recover, not several hours.
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.