Factual error: In circling over Washington Dulles, a plane would fly over several airports that they could land at with perfect communication, including Richmond, Baltimore, Andrews AFB, etc. Also, there is no communication from the airport to the plane but the plane would be in range of no fewer than 15 transmitting stations that could have relayed messages.
Factual error: When McClane is trapped in the cockpit of Esperanza's plane, and the terrorists throw grenades in, it sure takes them a long time to explode. At least a good 20 seconds passes before he ejects from the plane and the grenades go off. Normal grenades would have gone off long before 20 seconds.
Continuity mistake: Bruce Willis is emerging from an underground air-vent when the plane with General Esperanza is landing. Initially the plane is coming on a direct course for him and he struggles to get out. In fact the front wheel is on course with and knocks the vent cover. But in the very next scene, the tire marks clearly show the front wheel passed to the right of the vent and so completely missed it.
Factual error: Near the beginning of the film when John McClane goes to the pay phone and calls his wife Holly on the airplane, that was impossible at the time. Those phones you see on the seats on the plane can only be used from the air to the ground not the other way around. Holly does answer on the plane phone and not on any cell phone she had in her purse.
Continuity mistake: In the beginning of the movie when John is sitting at a table in the airport smoking a cigarette, you see him notice the table with the 3 (2 white and 1 black) guys that are acting suspicious. When the black guy gets up to leave, he leans down and you see a hand grab a package. If you notice, the hand that grabs the package is white. Later when the two white guys leave, one of them leans down to grab the package and it's the same shot that was used when the black guy grabbed his package.
Factual error: When McClane (Bruce Willis) is brought into Capt. Lorenzo's (Dennis Franz) office at Dulles Airport for the first time, Lorenzo mentions that McClane was in violation of several District of Columbia laws. Dulles Airport is in Virginia, not DC, therefore any DC laws would not apply to Dulles. (Although VA may very well have similar laws about airport misconduct.)
Continuity mistake: When Mclane is desperately trying to get his fallen Beretta from the conveyor, he flicks the on switch to the conveyor. The terrorist then sprints down the conveyor to try and get the gun before Mclane, and you can see in the first shot of the terrorist running, that he is virtually at the gun immediately. The camera cuts to Mclane, and then back to the terrorist who is now significantly further away from the gun than he was before.
Continuity mistake: When Col. Stuart is talking to Gen. Esperanza on the walkie-talkie about what runway to land on, behind Stuart you can see one of his men walk up to the map of the runways. Stuart turns around and starts walking to the map and the guy isn't there anymore. When Stuart gets in front of the map, the guy comes up and tells him which runway Esperanza should land on.
Factual error: Since the terrorists have implausibly taken over all the radios at the airport, the good guys use the marker beacons to communicate with the airplanes. Even if they could be modified to talk rather than beep, marker beacons (outer, middle and inner) are on the approach path of a runway, and only transmit to an aircraft as it passes overhead. The signal is only picked up by an aircraft's marker beacon receiver, if so equipped. There is not enough time to get a message. Nor could a marker beacon be used to broadcast to a large number of airplanes. The outer marker is only 5 miles from the airport. At most, one airplane would be holding over the outer marker.