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.
Other mistake: Where does the fire in the gas pipes come from? Even though a lot of gas - and thereby pressure - is directed towards the power station, why do they blow up under ground far away from the power station?
Revealing mistake: When McClane goes into the icy room in the power station, look at the pipe to the side of the acrobat: it's in shot a few seconds and you can see that the writing on the pipe is reversed, revealing that in the editing room, the shot was flipped.
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: 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.
Factual error: Natural gas flows through a pipeline due to pressure differences. The main line is held at a high pressure, usually 600 psi or more, while the end user is at a few pounds or less. You can not "send all the gas" to a particular location. No matter how much you raise the pressure in the main line it will only flow through the open valve at the end users location.
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.
Factual error: The sound of an airbag detonating is very loud, even more so with two detonating at the same time, quite a bit louder than what was depicted onscreen.
Continuity mistake: McClane's head wounds move around throughout the movie. Especially the two red spots on the left side of his head change colour a lot.
Factual error: There are no toll booths, tunnel or otherwise in the area of Washington D.C. where the anti-helicopter car launch is supposed to have taken place.
Continuity mistake: During the final truck chase through Baltimore, several traffic lights are seen with lights in them. But all the power was off.
Factual error: When Gabriel turns off the lights in the tunnel, we see a shot of cars heading towards the police car as the lights turn off, and not one of them turns its headlights on. In reality, with that many cars in the tunnel, there'd be at least one that was fitted with auto-lights.
Factual error: If the natural gas could be rerouted to McClane's position at the national grids control center, there are two major problems. The gas would not self-ignite on its way there as pictured, and the sheer momentum of that massive amount of gas in those long pipes would cause a massive leak at the endpoint. However, after the first (relatively small considering the total energy in all the gas) explosion, everything goes back to normal without one giant amount of gas erupting.
Factual error: In several chase scenes that take place in Washington DC McLane and Farrell are driving around the city with buildings that are at least 40 to 50 stories tall. This is impossible as the Height of Buildings Act of 1910 prevents any building being any higher than 20ft more than the width of the street the said building sits on. The buildings seen in the chases are much too tall for this city to actually be Washington DC.
Continuity mistake: During the shootout at Matt's apartment John scrambles away from the refrigerator and pulls himself around the corner. The view is from behind John and his chest is facing the corner as he pulls himself around it. The scene jumps to a view from in front of John, yet he's somehow already turned himself around so his back is to the corner (this makes for an easier transition to using the corner as cover, but it messes up the continuity). He couldn't have done this since he was still in the process of pulling himself around the corner.
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.
Visible crew/equipment: In the scene where John and Matt are in the middle of an alley, with Matt using the mobile to locate the power hub, the crew can be seen from the reflection from the glass behind Matt.
Factual error: Just before the power plant explodes we are shown a scene where the natural gas pipeline is exploding on it's way to the power plant. The first explosion (while not actually possible) would have destroyed the pipeline and no more gas would have flowed to the power plant and therefore the power plant could not explode.
Factual error: When McClane "kills" the helicopter with the police car, as shown in the film, the car runs up the toll booth like a ramp and smashes into the helicopter. However, if you look, though the slab on the side is ramp-shaped, it is about 2 feet off the ground, so realistically, the car just should have smashed into the booth rather than shoot over it.
Chosen answer: Looks like a standard 5 mph speed sign to me. You can't read too much into that. In addition though, Bruce Willis has already stated in a few interviews that he'd be more than happy to do another one.
XIII