Continuity: When Cage and that big guy are making their escape, the big guy falls over the rail and Cage catches his gun and tries to save him.  In the last scene before he falls, Cage is holding on to the very last tip of the gun, but it shows a wide shot and he is holding a lot more of the barrel.

Revealing: In the shootemup scene in the hanger at the beginning of the film Pollux Troy shoots an agent in the stomach and the agent flies back - you can see the rope pulling him.

Other: When Troy (as Archer) goes to defuse the bomb, the #1 key lights up before he even presses it.

Continuity: When John Travolta is shot on the carousel at the beginning of the movie, the shot enters his back near his collarbone. When the camera moves back a second later, the bullethole is much lower.

Visible crew/equipment: When Cage throws Castor's brother through the ceiling window, there's a shot of him hanging from the edge of the broken window. The support wire can be seen in front of him.

Continuity: When they are at the airport a car and a bush disappear and reappear below the writing "Welcome to Southern California International Airport"