Audio problem: Just as McClane and Farrell are about to leave the Eastern Power Hub, Farrell goes on a long rant and his mouth does not match the words he is saying. [In the unrated version of the film, the rant concurs with Will's mouth movements, but the mistake is valid for the regular version.]
Factual error: During the chase with the semi, McClane is shown struggling to keep the truck under control with the freeway collapsing/blowing up all around him. He is shown making a left turn on a ramp, and the truck going up on 9 wheels, almost rolling. The shot cuts back to McClane steering left to to try to control the truck. If he were to steer left, as depicted, he would be guaranteed to roll the truck. If he was trying to get the wheels back down, he'd have to steer into the roll, or right, to bring it back on the wheels. At the end of the shot, you can actually see the stuntman brings the wheels down with a short right turn of the steering wheel. The similar entry in corrections is right, the person making the correction is wrong. During 15 years of driving a semi, I had a very similar situation with the truck almost rolling. I had to steer into the roll to bring the truck back on the wheels, not away from it, as the film showed McClane doing.
Continuity mistake: When John and Mai are fighting at the power plant, John tosses Mai up against a glass board. Her 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 pony tail. But as she begins to fight, her hair is once again undone and messy.
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.]
Audio problem: During the final chase scene when McClane takes control of the semi truck, you can hear the truck continuing to shift gears even though McClane is not completely in the driver's seat and nowhere close to the clutch or shifter.
Factual error: In the street scenes of Washington, DC, the cabs are Yellow Cabs. DC does not have a yellow cab system, but rather "gypsy" cabs that come in all colors. There are actually very few yellow-colored taxi cabs.
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.
Factual error: Just after the F35 shoots most of the top off of the cab and the back of the semi truck McClane is driving, there is a camera shot that pulls back from the front of the truck that shows large 1-foot diameter holes in the top of the engine compartment. The first problem is that the plane's bullets came from the side, not the top (not down through the engine hood) and the second problem is that the engine shouldn't still be running with multiple 1-foot holes shot into/through it - yet the truck continues to climb the incline.
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 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: 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.
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.
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: 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).
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.