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: 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: When McClane first brings Farrell to the Cyber division, McClane has a cut over his eyebrow that he gets from a fight scene later in the film. [This mistake is pointed out in the DVD audio commentary: this scene was filmed after said fight scene was completed. Still a mistake, though.] (00:29:00)
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: John throws Matt to the floor when Matt is first being shot at. John lays on Matt to protect him and you can see that John's legs are off to Matt's left and are lying flat on the floor. The scene cuts to a view that's from behind their feet and now John's legs are no longer flat on the floor, his lower body is turned and he is lying on his right hip. (00:11:20)
Continuity mistake: Near the end of the film FBI operatives rappel down from helicopters for speed and immediately enter the warehouse where John McClane and friends are. Almost immediately Bowman appears and vouches for the three left alive in the building. He got there very quickly considering his helicopter was still in the air when the operatives were landing.
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: At the end of the scene where Bruce Willis's own car is involved with a crash between a dustcart and taxi you can see his driver's door opening during the aerial shot after he has left the location. (00:24:25)
Continuity mistake: McClane's head wounds move around throughout the movie. Especially the two red spots on the left side of his head change colour a lot.
Continuity mistake: When McClane and Farrell are fired upon during the escort to DHS, Agent Johnson is killed and slumps against the steering wheel, and in the next shot the deceased's foot slips off the brake so the car jolts forward and hits the FBI's SUV in front of them. Four shots later, in the interior shot from the back seat directly behind McClane ducking inside the car, we see Agent Johnson sitting upright very much alive, at the left side of the screen. (00:38:35)
Continuity mistake: During the final truck chase through Baltimore, several traffic lights are seen with lights in them. But all the power was off.
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: At the start of the chase between the HAZ-MAT van and the semi truck, McClane hits a couple of cars and seriously damages the front drivers corner of the truck. In later shots, the damage has gone. (01:48:55 - 01:51:50)
Continuity mistake: During the shootout at Matt's apartment John scrambles away from the refrigerator and pulls himself around the corner. The view is from behind John and his chest is facing the corner as he pulls himself around it. The scene jumps to a view from in front of John, yet he's somehow already turned himself around so his back is to the corner (this makes for an easier transition to using the corner as cover, but it messes up the continuity). He couldn't have done this since he was still in the process of pulling himself around the corner.
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)
Continuity mistake: In the scene after the power plant explodes and Farrell is giving his "What is the point?" speech, his hair changes several times between shots, from hanging down in front of his face to being swept to one side.
Continuity mistake: When McClane knocks the fridge over so it's on its side near the start, his head is above the top (side) of the fridge. Camera cuts and it is well below the top (side) of the fridge. (00:12:45)
Continuity mistake: During the traffic jam scene, when the truck crashes against the taxi, the view inside McClane's car shows the taxi colliding against the car, dragging it away violently. From the aerial angle, the taxi doesn't touch McClane's car at all. (00:22:35)
Continuity mistake: In the traffic jam in the beginning of the film (right after all the lights have changed to green), the car next to McClane's is black/dark. But a few seconds later when you see it from a helicopter, it has changed to white. (00:22:30 - 00:23:30)
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)
Answer: The radio line mentioned the officer's name in the seconds after Gabriel's voice recognition picked up Farrell's name.