Factual error: I'm afraid John and Zeus are in for a very nasty surprise when John uses a few drops of the binary explosive to blow apart Zeus's handcuffs. We know the explosive is sensitive to shock or impact, like nitroglycerine - we see samples being detonated by being hit. So, when John detonates those few drops it will set up an adiabatic shock wave, and since the binaries have mixed at this stage that is going to set the whole lot off. It's called a sympathetic explosion. Those two tiny drops are certainly enough - they couldn't possibly cut hardened steel if they weren't.
Revealing mistake: When they are being chased in the Mercedes, McClane tells Carver to pull the fuse for the anti-lock brakes. When Carver says he won't know which fuse is which, McClane tells him to pull them all. If Carver were to do this, he would cut electrical power to critical functions, such as the fuel pump or ignition system.
Factual error: When you see McClane and Zeus being chased by the Germans in the pickup truck, you figure they're being chased somewhere around the Henry Hudson Parkway because you see all the trees. After they kill the Germans and McClane is "interviewing" the dead ones, you can see behind Zeus the exit 29 sign for Greenwich/Lake Ave., which is actually located on the Merrit Parkway about 20 to 25 miles away, north of the city. When McClane picks up the quarters again, you can see the exit sign again.
Continuity mistake: In the taxi scene were you see the ambulance escort pull onto the road; you see John swing around a corner going very fast, when Zeus says "slow the fuck down McClane". He gets ready to pass a large black car but the next shot (an in car shot) you can see that he never passes the car.
Continuity mistake: When they drive through the park and jump off the rock they land on a pile of leaves which covers the hood. Some of those leaves fall off but not all of them - in the next shot the hood is completely clean.
Continuity mistake: There is a scene where Samuel L. Jackson and Bruce Willis are in a crowded park, and they have to defuse a bomb by measuring out water. Before they do that, he picks up a cell phone and calls a bad guy with it. When he is beginning the conversation, the cell phone antenna is down. They change to a different angle, and the antenna is up.
Continuity mistake: When Willis washes the blood off his face after shooting the bad guy in the elevator, the "towel" he wipes his face has no blood on it at all. Even after washing the worst off with the water it would still be full of blood.
Other mistake: The winch attached to the front of the black pickup isn't particularly big, and its size governs how long the cable can be. From a side shot of the winch cable stretching from the pickup to the boat, there's no way the cable being shown comes from the winch on that truck: it's too long, it would never spool back onto the winch.
Audio problem: During the heist in the Federal Reserve a lot of sounds are missing. For example, when Katya drops her bolt cutters, there is no sound as they hit the ground.
Revealing mistake: When the truck is being pulled off of the bridge by the ship, if you look closely right before the truck plummets towards the water, there is no engine, transmission, or anything else in the engine compartment of the truck, which was left exposed after the hood fell off in an earlier wreck.
Revealing mistake: Right after the explosion, when Simon walks up to a detective and introduces himself as an adjuster for the bank, he asks if the detective can show him the way down. When the detective says yes he calls over an officer Murphy, who is facing the crowd. Murphy is already looking back and begins to walk to the detective before he is even called for.
Continuity mistake: When Samuel L Jackson runs down the stairs in the subway station, he checks the clock, which reads 10:19:10. Then when the train destroys the clock a bit later, the time's now 10:20:24, though well over 2 minutes has passed (only counting Samuel L Jackson's scenes, as Bruce Willis' presumably take place simultaneously. Counting them separately it's even longer). (00:33:00 - 00:36:30)
Continuity mistake: When Bruce and Sam are driving through the park and jump the concrete ramp out into the street, they land (or drive over) 2 taxi cabs parked there. In the close-up shot of their taxi crushing the front and rear of the other 2 parked ones, you can see that an entire wheel disconnects from one of the parked taxis and begins to fling out into the street with great speed. In the following wide-angle shot of their taxi swerving into the road, that wheel is nowhere to be seen. It should have bounced across the road.
Visible crew/equipment: In the taxi scene, you can see that the taxi is abnormally high, and there's a special strut rig under the front part of the car so it doesn't take a destructive beating in that whole racing scene.