Factual error: When McClane "kills" the helicopter with the police car, as shown in the film, the car runs up the toll booth like a ramp and smashes into the helicopter. However, if you look, though the slab on the side is ramp-shaped, it is about 2 feet off the ground, so realistically, the car just should have smashed into the booth rather than shoot over it.
Continuity mistake: After Mai kicks McClane out the window at the power hub, there is a shot of her turning and walking away. This is obviously a reused shot of when she walked away from beating up McClane only a minute or so earlier - obvious signs are that her facial bruises have vanished and her hair is perfect, and then when it cuts to her grabbing Matthew, the bruises are back and her hair is messy again. (01:07:50)
Continuity mistake: In one scene we see the map of the power grid of Eastern Sector shutting down. All sectors are red. A few scenes later we are in Warlock's basement. He has the same map on one of his screens, but there some sectors are red and some are green.
Continuity mistake: When John and Matt are in the patrol cars and Gabriel has them rerouted to a blocked road, there are no cars on the road besides the patrol cars, but throughout the scene when the camera cuts you can see traffic moving smoothly along with them.
Continuity mistake: During the final chase, the right front tire of the Freight liner is flat at one point after hitting a number of parked vehicles. The next shot showing the front of the truck shows the tire is fine.
Continuity mistake: The hacker slaps McClane's daughter moving her head to the right, hair messy around her face. The immediate angle from the hacker's point of view shows her head tilted to the opposite direction, with her hair perfectly brushed.
Factual error: The F-35 JSF is shown having 2 guns coming from the side of the intakes and can fire for a long time. The M61A2 Vulcan Cannon on the JSF is above the left air intake and can only fire for 4.8 seconds before it runs out of ammo.
Audio problem: When Gabriel is starting to move out with the large truck, you hear the sounds from the truck tires but the tires aren't moving.
Continuity mistake: In the semi chase scene when Bruce takes control of the truck he initially shoots twice through the door and you see two 'bullet holes'. When the cut to the cab the driver is shot 5 more times. After Bruce throws out the driver and closes the door you only see the two original 'bullet holes'. There should be about seven of them.
Other mistake: When Gabriel looks at McClane's police record it mentions McClane receiving a commendation for the Chicago airport incident in 1990. That incident happened at Dulles Airport in Washington D.C., not Chicago.
Plot hole: When Lucy is stuck in the elevator, and they re-activate the elevator and turn all the lights on, Lucy should have been able to push the buttons and get to the floor. She did not have to wait for someone to rescue her.
Factual error: In the scene with the traffic jam in DC the traffic lights are green in all directions. Traffic lights are built with a mechanical stop that prevents this from happening.
Factual error: At the power plant the natural gas is shown burning inside the pipeline. Natural gas pipelines are void of oxygen. No matter what the temperature or pressure in the pipeline the gas would not combust.
Factual error: McClane is able to stand on a jet with its engines on but it would be way too hot to do that.
Continuity mistake: As McClane is powering up the helicopter to fly to Warlock, the rotors are already up at full speed. The next cut shows the helicopter in full from outside with the rotors turning much too slow compared to the previous and following scene.
Continuity mistake: When being escorted by the FBI near the beginning, they are in an FBI car which is plain white. They then get shot at by the helicopter and are seen speeding away in the FBI car. A few shots later this car becomes a normal police squad car.
Other mistake: In the scene in which McClane and Farrell are in the car on the way to the Eastern Hub, the shots alternate between looking at McClane then looking at Farrell. When the stars are in profile there is visible through the subject's car window the landscape passing by, but the same hill appears outside each window. (01:00:55)
Continuity mistake: At Woodlawn, after McClane takes Russo out and taunts Gabriel over the radio, Gabriel sends Rand after him, saying, "Kill this guy, and I'll give you Mai's share." But four minutes later, when Gabriel has Lucy talk to McClane on the radio, Rand can be seen standing casually against the wall behind him, even though he already left. (Timecodes from unrated edition.) (01:39:20 - 01:43:25)
Continuity mistake: When Running to the car after the apartment shootout, Farrel gets in the car and McClane is not around by the car as we can see the car. However when Farrel shuts his door, McClane is already in the car. In the previous shot we could see McClane behind Farrel. (00:15:35)
Continuity mistake: When you see all the power going off, you see the same clip being used twice. The power goes off, it shows the airport and hospital, then it shows the power going off in the same place again. (01:14:40)
Answer: The radio line mentioned the officer's name in the seconds after Gabriel's voice recognition picked up Farrell's name.