Other mistake: When they're running away from the embassy because of the bomb threat he uses his key chain remote to shut off the alarm to his car. Then when they get in there's an envelope, the proof of life, on the floor. The sister asks how they got in. That's a good question. The alarm was on. How did they get into the car?
Other mistake: When Russell Crowe kills the bad guy just before the attack begins, he uses the serrated blade of a Leatherman tool to slit the guys throat. Any special forces soldier would carry and use a killing knife like a Gerber or Ka-bar, or at least use the standard blade on a Leatherman tool.