Factual error: When McClane and Zeus take the little hatchback from the bank location, they run up the ramp by the Brooklyn Bridge and McClane looks to see the dump trucks aren't on the bridge. Zeus then spots them on FDR Drive and they speed off down the ramp to FDR Drive. The ramp they were on doesn't connect to the ramp they took to give chase. It only heads towards City Hall or over the bridge. They'd have to take the Civic Center ramp, do a u-turn under the Brooklyn Bridge approach then head back up the ramp to FDR Drive.
Visible crew/equipment: There is a shot towards the end of the film, (just before Willis and Jackson exchange dialogue in the engine room) in which it shows the entourage of people boarding a smaller boat from the much larger ship. Look towards the bottom left corner of the screen as the boat pulls away - inside you can see the head of a female boom mike operator.
Continuity mistake: When the two heroes are crashing through the city in the taxi, the car takes a significant beating. The bumper is pushed up from rough landings and there are long scrapes down each side. When Zeus skids to a halt outside Wall Street station the taxi is in almost perfect condition.
Revealing mistake: When the female terrorist goes to use the large drillhammer on the concrete wall, the force of turning it on causes it to "jump" in her hands. When the drill bit bounces against the concrete wall, you can clearly see the wall move back and forward about half an inch.
Revealing mistake: When Willis is driving through the park, you can see the tyre marks and lines where they had driven there on other takes.
Factual error: When Bruce Willis and Samuel L. Jackson are in the minivan with the feds, the bad guy rings up. This call is taken on an old Motorola flip phone. They plug it into something to make it hands free loud speaker. The thing they plug it into is actually the house charger that comes with the phone, it doesn't have a loud speaker and it's also mains voltage. You can even see the spare battery in the second slot at the back of the charger and the red LED flashing to indicate that the battery is charging.
Factual error: In the North of the Border scene when McClane's helicopter makes an emergency landing you can see a Giant Food trailer in the background. They are supposed to be in Canada, but this grocery store chain is located in the Mid-Atlantic states. This scene was actually filmed in Jessup, MD where Giant has its headquarters.
Deliberate mistake: While most of the German spoken in the movie is correct (even if with bad accent) there is a translation error in the scene at Yankee Stadium. The accent suggests that these bad guys were raised in the communist eastern Germany and previously served in the secret service "stasi." When the guy with the sniper rifle gets nervous and asks if he should shoot or not, the other one says,"Nein, wir brauchen den anderen", which would translate, "No, we need the other one", but the subtitles say, "We'll follow him", which they do.
Continuity mistake: When McClane and Zeus are chased after escaping from the aqueduct, look at the right front light of the Dodge Ram the bad guys are driving. It goes from being broken to intact several times. Also, when McClane and Zeus stop the same Dodge Ram afterwards on the bridge, both front lights have magically become intact again and even though now the hood is missing, it's still obvious that the whole front part of the truck is significantly less damaged than before.
Continuity mistake: In the park with the water riddle, just before they argue about Zeus being a racist, you see both jugs. The 3 gallon jug is empty and the 5 gallon is possibly 3 gallons full. Then they argue. By the end of the argument, John says that the 3 gallon jug is exactly 2 gallons full and you see that the 5 gallon jug is full up, giving them the answer to the riddle.
Continuity mistake: When they first start with the gold operation, Targo jumps on a large orange vehicle with some kind of drill on the front, already raised into the vertical position. He then jumps off and in the very next shot the drill raises from a horizontal to vertical position.
Continuity mistake: Towards the end, when Bruce Willis notices the writing on the aspirin bottle, he leaves it in the phone booth and the camera jumps towards it a couple of times. In the first shot the writing's almost vertical, but in the following shots it's at a definite angle. (01:48:35)
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.