Deliberate mistake: While McClane drives in the tunnel, Gabriel orders, "Open the gates on the north side entrance." A few shots later the signal light changes from red to green and the north gate opens. The "warning" sign is backwards in this flipped shot. Then, when Gabriel opens the gates at the south entrance, there's a proper shot of the "south" gate opening. The two shots of the "north" and "south" gates opening are the same, but one is reversed. All the dirty smudges on the signs, booths, etc, are identical. (00:41:20 - 00:42:05)
Continuity mistake: When the truck crashes into the pillar that McClane and Matt are hiding behind in the tunnel, we see a large portion of the pillar fall off from the left side. However, when McClane gets up to drive the police car, the pillar is in perfect shape. (00:41:30)
Plot hole: When in the tunnel, McClane gets back into the cop car and leaves Farrell, he drives very quickly. After the helicopter blows up, it is only a few seconds before Farrell finds McClane. Even running at his top speed, Farrell could not have reached McClane's position so quickly. (00:42:00)
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: In the scene when Bruce Willis is driving the police car up the ramp to blow up the helicopter, the guy jumps out. As he jumps out he has got headphones on, but when he lands on the car they fall off. The next scene it shows him taking them off. (00:43:45 - 00:44:40)
Continuity mistake: John's face is all bloody after he rolls from the car and "kills a helicopter with a car". The blood on his face constantly changes during the shots. Sometimes there is blood all over his face, sometimes there is quite a bit less. Sometimes he has blood streaming from the cut on his nose, sometimes there is nothing on his nose. The blood changes back and forth, so it's not just him wiping the blood away from his face (and his hands are by his sides during all the shots). (00:44:35 - 00:45:30)
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: 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: In the scene where McClane rebuffs Ferrell for thinking it would be cool to do the firesale, you can see pipes for firehoses right behind McClane. When the shot changes to a long alley shot, the pipes are a good ten feet away, but when it reverts back to a closeup, the pipes are back to right behind McClane. (00:55:20)
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: McClane rips the airbag out and tosses it on the road. When they drive away, the airbag has gone. (00:57:30)
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: When John and Mai are fighting at the power plant, John tosses Mai up against a glass board. Her half pony tail has come undone and her hair is a big mess. You see Mai from the back as she gets up to come after John. Her hair is now neatly combed and back in a half pony tail. But as she begins to fight, her hair is once again undone and messy. (01:06:45)
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: When McClane is strangling Mia, the way he holds the cable constantly changes. (01:08:05)
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 McClane is on the phone to Boeman about Thomas Gabriel, the blood on McClane's hand is constantly changing. (01:12:15)
Continuity mistake: In the semi truck that John is driving towards the end of the film, one scene shows the truck has a automatic gear box control box, in another he is changing gears on a manual shift. 2 different trucks. (01:14:15 - 02:13:40)
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 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.