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.
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.
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.
Trivia: One of John Woo's directing styles is to mark large action sequences with doves. You can see this in Mission: Impossible 2, on the island just before the final action sequence and in the church after the funeral in Face/Off.