Corrected entry: When Bruce Willis throws the C4 (stuck with a chair and a computer screen) down the elevator shaft, the C4 explodes. C4 is very manageable and won't explode through physical force; even a bullet won't make it detonate. You'd need the blaster caps or some other explosion to set the C4 off. For more info on C4, read this: http://science.howstuffworks.com/c-42.htm.
Corrected entry: It's been pointed out that McClane's shirt changes from white to green after he emerges from the vents; this is certainly a "cheat" by the wardrobe department to make him appear grimy and battle-worn. But notice, also, that toward the end of the film, the shirt switches back to white.
Correction: Towards the end of the film he's not wearing a shirt at all.
Corrected entry: Towards the beginning of the film, John enters Nakatomi Plaza and finds Holly's name on the computer so the guard can tell him where she's located in the building. After John does this, the guard tells him that she's on the 30th floor and that there's no one else left in the building. Now, why couldn't he have just told him that the party was on the 30th floor and saved him the trouble of playing with the computer?
Correction: This is a list of people who are currently checked into the building, so obviously the guard is having him check if Holly is actually there at all, not to see where she is.
Corrected entry: Towards the beginning of the movie, Bruce Willis notifies the cop outside that there are 12 terrorists. However, if you tally the numbers as he takes out each one, you wind up with 13.
Correction: When does he say 12? He says "unknown number of terrorists...at least 6." Later he says " They're down to nine now, counting the skydiver you meet."
Correction: John only sees twelve of the terrorists. The 13th is the Computer Expert, Theo.
As a point of fact, John sees Theo in the scene where Takagi is killed. Karl and Theo are both in the room during that scene.
Corrected entry: It seems to me that alerting the enemy to his presence with the "ho ho ho" stunt was a pretty stupid thing to do and not what a trained officer would do. Without this, the terrorists may have believed that the new fire alarm system had malfunctioned but this made it clear that he was there.
Correction: Even if they did think that initially, when the terrorist didn't return, suspicions would have been raised.
But it would've given John more time to plan what to do next. Or give him time to address the situation.
Corrected entry: The black police officer keeps giving information about the police activities to McClane over the same frequency that he knows the terrorists are using. I also doubt he would be allowed to just use the police radio for chit-chat in such a situation.
Correction: The officer could argue McClane is someone 'on the inside' - i.e. someone who knows the situation well and can be trusted. As for the frequency, the radio may be designed to transmit on several frequencies - the frequency that the Police use will almost certainly be one (in case of emergencies).
Correction: My understanding of the scene was the monitor was there to ad weight to the chair and keep the C4 in place. The detonators set off the C4, not the computer monitor.
Rlvlk
The detonators won't randomly set off the C4. That's not how detonators work. The mistake is accurate.
Not "randomly". CRT screens / capacitors famously store a dangerous level of electricity for a long time after being turned off, and smashing the screen / damaging them will be enough to discharge it, which would in turn trigger the detonators and thus detonate the C4.