Continuity mistake: McClane's fireman's jacket gets progressively bloodier throughout the film, but around the time when he is fighting the terrorists on the planes wing, it is miraculously clean again. McClane is not wearing it, but it does get cleaner. (01:45:50)
Ssiscool
Continuity mistake: In the airport lobby, when the two policemen come at the bar they have "snow" all over their clothes. In the next shot they are shown from behind sitting at the bar and Lorenzo's brother has no snow on his jacket. Seconds after Mc Clane comes to talk to them and the cop has snow on his shoulders again.
Continuity mistake: When McClane grabs Marvin the janitor and pushes him against the lockers, McClane's thumb changes position on the gun, some shots it's on the hammer, other shots it's around the handle.
Bishop73Continuity mistake: When the general exits the plane with Colonel Stuart, nobody shuts the door. It is closed in the very next shot.
manthabeat 
Answer: They were placing devices that monitored the radio and phone chatter at the airport. That is why the "bad guys" always knew what the "good guys" were up to. I say devices becuase they placed two devices as the "decoy" one is found later by one of the soldiers.
XIII