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.
Factual error: When the collected bad guys are at the "North of the Border" truck stop, a subtitled henchman tells Jeremy Irons that the helicopter will be ready in ten minutes. But the confused fellow actually says, "in zwanzig minuten," which means TWENTY minutes.
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.
Factual error: This film perpetuates the Hollywood myth that being shot in the upper leg is a minor inconvenience and will leave you with a slight limp and not much else. Simon shoots Zeus in the thigh with a Heckler and Koch MP5K from a range of about a metre. That would almost certainly shatter his thigh bone and rip through his femoral artery. In the unlikely event that Zeus was lucky enough to avoid any such injuries, he wouldn't be walking anywhere for months.
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.
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: The security guard at the vault door fires a few shots from his handgun (about 6) down the hall towards Simon and the other terrorists. He then loads one of the shotguns and calls for help. After finding that the front guard was a terrorist he fires 14-15 rounds from the same shotgun before he is killed. The problem is that it was a Remington 870. Like most shotguns that size they only hold 8 rounds, or 9 if one is chambered.
Factual error: Typical for action movies. Willis and Samuel L. Jackson couldn't have possible survived the explosion of the ship being in the water or not. If the heat didn't get them the pressure wave would have.
Factual error: A picky, only-a-New-Yorker-would-care point: When Bruce Willis goes down into the subway, it's supposed to be the 1/2/3 lines (West Side trains). The station filmed is actually the 8th Street stop on the N/R (Broadway) lines; it's right by NYU.
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.
Chosen answer: He sees the reflection of his friend's badge number that he remembered from their conversation about the lottery earlier, so knows the badge was taken from his dead friend.
Captain Defenestrator