Continuity mistake: During the cemetery scene where they visit the son's grave, you see a wide shot of them walking between the stones. There are leaves on the trees and neatly trimmed grass. When we see a close up of the stone and the plaque in the ground, a hand reaches down to brush the leaves off so they can read it, and there are dead leaves all around - but there were no leaves on the ground in the wide shot.
Continuity mistake: When Castor (as Sean Archer) grabs the speargun shaft before it can unload, he takes a piece of glass and begins to cut his face. The broken glass has a small circular piece missing from the edge, but from a different camera angle that small piece is more intact than the previous shot. (02:09:15)
Continuity mistake: When Castor Troy (as Sean Archer) says, "Every time you'll look in the mirror, you'll see my face," he proceeds to cut his face. The first cut he makes is straight down the side of his right cheek (viewer's left) and later that cut is curved and closer to his nose. This may appear to be a mistake at first glance; however, Castor's facial expression is different in the two images. When he made the cut, the cheeks were pulled away from the nose; in the second photo, the muscles are relaxed, moving the cut closer to the nose. (02:09:15)
Continuity mistake: After the surgery, when Sean (as Castor Troy) breaks the center mirror of the tri-fold mirror, what remains are the two side mirrors and white backing within the center frame. When Tito grabs him as he starts cursing, in these close-ups the reflections seen are as if all three sides are still intact. (00:37:15)
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)
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.