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.
Factual error: When Zeus goes to Yankee Stadium, the terrorists tell him to report to the home-team dugout. Yet when Zeus goes to Yankee Stadium, he is shown at the dugout along the third-base line, which any Yankee fan knows is the visitor's dugout. Given he knew which dugout he was meant to go to, and the importance of the situation, this can't just be a character mistake.
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.
Revealing mistake: When fighting with Targo on the boat, McClane pulls a chain, which trips Targo over. When we see Targo being tripped from above, you can see it is a stunt double - not only is he bigger than the actor playing Targo, but also his hair is grey unlike Targo's brown.
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.
Factual error: The entire plot is based on the idea that they're going to steal $140 billion worth of gold. At a gold price of $300/ounce, that's 14,500 tons of gold - how's the suspension on those dump trucks? There's no way trucks like those could carry over 1,000 tonnes each, but Simon tells McClain there is $13 billion worth of gold in the back of McClain's truck.
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.
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: 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 then over the bridge. They'd have to cross the bridge, do a u-turn in Brooklyn then come back across to Manhattan.
Other mistake: After McClane hits Targo with the chain and knocks him out, McClane searches him. Targo's body is not only in a different position, but the chain is wrapped around his head, which McClane never did.
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.
Continuity mistake: In Harlem, when Zeus gets his arm cut by the black dude wielding the switchblade, another black dude is swinging the bottle toward McClane's head-with his left arm. The following scene, McClane gets his head injured from the same bottle wielded by the same dude-only this time wielded by his right arm not his left.