Continuity mistake: When Chuck and his compatriot are escaping from the terrorists in the Greek Orthodox Church van we see Chuck leaning out of the side of the van until the sliding door is hit with three shots in a near straight line, however, the next time we see the side door panel it is undamaged until subsequent shots which show a square grouping of four holes instead of a line of three.
Continuity mistake: During the scene where the hijackers have demanded all passports be collected by the flight attendants, pay close attention to the part where right after Ben Caplan is called to the front. Right behind Caplan's seat is a bald guy with glasses who hands Ingrid his passport. A few minutes later, Ingrid is approached by 3 Marines stating that they don't have passports and instead have Navy Id's, and right as she says, "Put them away", the same exact bald guy with glasses a few rows back can be seen holding his passport above his head.
Continuity mistake: When one hostage is leaving the plane his daughter gives him her doll. Several times when they show the hostages he has the doll, even when they arrive at the airport after being rescued. As they are boarding the plane to leave you see him walking without the doll, but he has it when they land in Israel.
Continuity mistake: Norris is on the motorcycle and aims the rocket at the car. First scene, shows it shooting out on the left side. Second view it's on the other side.