Continuity mistake: When Samuel L Jackson runs down the stairs in the subway station, he checks the clock, which reads 10:19:10. Then when the train destroys the clock a bit later, the time's now 10:20:24, though well over 2 minutes has passed (only counting Samuel L Jackson's scenes, as Bruce Willis' presumably take place simultaneously. Counting them separately it's even longer). (00:33:00 - 00:36:30)
Continuity mistake: When Samuel L Jackson is at Yankee Stadium, there is a close up shot of him and in the background you can see the water hose used by the grounds keeping crew. Moments later, when the camera is on a further shot, you can see that the hose is gone. (01:20:50)
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)
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.
Continuity mistake: When Bruce Willis swerves into Central Park, he pulls the steering wheel hard left, but the next shot shows the car turning right.
Continuity mistake: When McClane is thrown out of the aqueduct he jumps into the Mercedes driven by Zeus. Then another car shoots at them and they're in a fight. If you look at it closely, the front window of Zeus' Mercedes is broken, but in the next scene it is like nothing happened.
Continuity mistake: In the scene where McClane jumps in the car because the Germans are shooting at him the first shot he gets in and his feet are all the way in. But in the next shot his feet are still out and then he brings them in again.
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 McClane is entering the subway, a man in a suit and a blond woman in a red dress pass behind him twice.
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: In the beginning, when the big explosion occurs, watch the 2 last shots. Close shot from two blocks away: Big traffic jam. Wide shot from above: Half of the cars have disappeared from the same spot.
Continuity 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.
Continuity mistake: In the car chase scene where the Germans are in the Dodge Ram and Zeus and John are in the car, during the mid point of that scene you'll notice the ram has a hood, and a few seconds later it is missing it.
Continuity mistake: While in the police station, a chubby guy brings the suitcase with the liquid bomb and to explain how it works he dips a stick with the liquid and throws it away to make it explode. Watch now the guy behind him covering his hears: Headset off, then he puts it on; then suddenly, in a very brief shot, when he is behind the chubby man, the headset is off again. In the next shots he has it on.
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.
Continuity mistake: When the police van leaves McClane semi naked on the street, his beard is a mere shade. When he mets Zeus, 10 minutes later, his beard has grown much larger.
Continuity mistake: When the police get to Chester A. Arthur school and the kids are all in the auditorium, we see Detective Lambert walk into the auditorium wearing no badge in his jacket pocket. In the very next shot, he is wearing it again.
Continuity mistake: There is a big stain of wet blood on the back of Zeus just after McClane burns the cuffs to escape from the bomb on the ship. When they run outside the stain is dry, smaller and blurry.
Continuity mistake: During the car chase between the Ram and the Mercedes, the Mercedes is going around a red Plymouth Acclaim, but in the very next shot it is a Chevy Cavalier. The Ram truck then starts scraping between the wall and the other side of the Cavalier, but when it cuts to a close-up it is now hitting the side of a grey Buick that was in front of the Cavalier.
Answer: And Zeus mentions about brothers knowing how to shoot guns.