Continuity:
Simon supplied two tickets to the baseball game, even though Zeus didn't join McClane until later.
Continuity: A guard at the Federal Reserve Bank fires more than five times from a shotgun which only holds five shells.
Factual errors: A truck full of gold would weight about 300 tons, and would have extreme difficulty travelling up the indicated ramps. Additionally, Zeus would not have been able to wield a solid gold bar as he apparently did when smashing the car window.
Continuity: A sign in the subway scene indicates a Tuesday, yet dialogue in Zeus' nephew's school indicates a Friday.
Errors in geography: The Number 3 train that McClane boards at the corner of Broadway and 8th would take him further west, not in the direction indicated. Also, it does not stop on the corner of Broadway and 8th.
Crew or equipment visible: When the Mercedes rolls, it is possible to see on the upper right hand side of the screen the wire which pulls the car over.
Continuity: A terrorist says "Zwanzig" ("twenty"), which the subtitles translate to "ten."
Continuity: A terrorist in the stadium says "Wir brauchen den anderen noch." "We also need the other one" which the subtitles translate to "Well follow him."
Continuity: The level of water in jugs during the argument about racism.
Revealing mistakes: Obvious stunt taxi driver, not McClane.
Continuity: Despite being squashed between a wall and a truck, the taxi doesn't show any scratches on the side.
Continuity: The terrorists' Dodge truck that chases McClain and Zeus in the Mercedes changes at least 10 times during the scene. Headlamp covers disappear then reappear, the truck's wheel style changes, and finally, the truck gets larger off-road type tires and wheels. Also, the winch cable on the truck is unrealistically long.
Errors in geography: When McClane and Zeus inspect the toppled truck after dispatching the terrorist occupants, supposedly on the Saw Mill Parkway in Westchester County, we see an exit sign for Cos Cob. Cos Cob is part of Greenwich, Connecticut, more than 10 miles away and not sufficiently important to have a sign at that distance.
Errors in geography: The ship travels from Hudson River to the middle of the Long Island Sound in an impossibly short time.
One might also notice that when Willis' character examines the last two rounds in his revolver, holding them in the palm of his hand, they look -alot- like the more photogenic .45Auto Rim than the .38 Specials they are supposed to be.
Same in the first Die Hard movie. Before shooting Hans, he examines two bullets held in the palm of his hand. Supposedly 9mm, they look -alot- like the larger .38 Super. Guess regular 9's would have looked wimpy.
Toward the end of the movie John McClaine (Bruce Willis) blows up the bad guys who are in a chopper. He does this by shooting a live wire connected to a building. This amazing shot was made on the first attempt, in a dark area and under great stress (not to mention the bad guys shooting "live" blanks at him), with a .38 caliber snub nose revolver. If all Hollywood actors are such great shoots why are they not the next Olympic champions in all shooting events (Imagine them with a free pistol)?
When the terrorists are breaking into the Federal Reserve Bank's underground vault, the hapless marshal gets at least a dozen rounds out of his Mossberg pump without reloading. While the (presumably 9mm) rounds from Bruce Willis' Beretta can penetrate a dump truck bed laden with gold bullion, the rounds from the baddies H&K's that perforate Bruce's Mercedes miraculously lost their lethality.
