Continuity mistake: While McClane and Farrell are in FBI Police car 279, the windshield's rearview mirror repeatedly vanishes and reappears. (00:38:25)
Continuity mistake: During the traffic jam early in the movie, John and Matt get out of their car and walk away on foot. In the next aerial shot looking down, you see someone stepping out of the very same car they were in. (00:25:27)
Continuity mistake: When driving the semi, McClane collides with the rear of a black BMW, but when the camera shifts to a different angle the collision continues with a cut of the truck hitting a Mercedes from earlier in the scene. (01:48:50 - 01:51:45)
Continuity mistake: When inside the stationary semi-truck the actors are swaying and moving as though the truck is travelling, but it has not yet left the warehouse. (00:50:00)
Continuity mistake: During the plane and semi scene the front of the semi gets shot to pieces. If you look at the windscreen when the semi comes back onto its wheels it's more like a protection cage, then in the next shot it's gone.
Continuity mistake: The wounds on John's right eyebrow and cheekbone change size, disappear, and switch from fresh to dry then back again throughout the film.
Continuity mistake: When John drives over the fire hydrant and the water jet hits the helicopter, the gunman falls out and ends up on the ground between the car and water jet. When John drives off in the long shot his body has disappeared.
Continuity mistake: When McClane is on the phone to Boeman about Thomas Gabriel, the blood on McClane's hand is constantly changing. (01:12:15)
Continuity mistake: When talking to AV-81 Gabriel's microphone has a wire round it. The position of the wire changes instantly. (01:47:50)
Continuity mistake: Throughout the film, the injury to Farrell's ear constantly changes severity. (01:42:10)
Continuity mistake: Just after the explosion at the power centre, Farrell's hair changes from messy to neat when he says "Win? When did we start winning?" (01:14:20)
Continuity mistake: When McClane and Farrel are talking about what Farrel would do next if it was his fire sale, McClane and Farrel move closer together instantly. (00:54:00)
Continuity mistake: When John and Lucy are having an argument at the start of the film, Lucy's hair is over her shoulder or not over her shoulder, depending on the shot. (00:04:20)
Continuity mistake: When the 4x4 drops in the lift shaft, Ferrel is stood by the side of the door. Then as he says "Did you see that!?" he has changed position instantly. Then he's back to the position he was in before. (01:09:25)
Continuity mistake: When in the traffic jam, just before the first accidents, the background doesn't move in the shots of Ferral, but it does, and quite fast, in the shots of McClane. (00:22:00)
Continuity mistake: When McClane is strangling Mia, the way he holds the cable constantly changes. (01:08:05)
Continuity mistake: When he's talking to Ferral about a fire sale and what would be next, the cuts on McClane's face are constantly changing. (00:55:35)
Continuity mistake: When in the tunnel after blowing up the helicopter, John has got blood all over his face. However the amount of blood and the position of the blood keeps changing. (00:43:20)
Continuity mistake: When McClane tells Matt to get ready to run when in the apartment, McClane's position changes instantly. (00:14:05)
Continuity mistake: McClane's shoulder holster disappears while fighting in the hanging truck in the elevator shaft. We can see he has the holster again (albeit a different kind) before the fight with the parkour guy.
Answer: The radio line mentioned the officer's name in the seconds after Gabriel's voice recognition picked up Farrell's name.