Continuity mistake: When Miranda Frost finally gets killed, her right arm goes from being held up, then outstretched when she gets kicked, to up just before she falls over, to outstretched as she actually does fall over. (01:55:15)
Continuity mistake: In the US Command Bunker, when the group gathers in front of the large satellite monitor on the wall to discuss Graves' whereabout, the shot from behind shows a man in business suit already passing Bond completely; when cut to the front in the next shot showing Bond's face, the same man is seen crossing right behind Bond again. (01:46:13)
Continuity mistake: In the scene where Bond's new car is introduced to him, Bond can't see it, even though it moves, but when Q walks past it, it distorts the image quite a lot. Further on in the film, whenever the car is invisible, it distorts the image behind it.
Continuity mistake: When Q hands Bond his new watch, he puts it on his left wrist, as the Pierce Brosnan "Bond" always has. Every scene from there after shows it on his left wrist. However, when he later removes it to use the laser emitter to cut a hole in the ice, he removes it from his right wrist. All following scenes show it again on his left wrist.
Continuity mistake: When James is first talking to Jinx after she comes out the water, her hand position changes on the glass she is drinking from.
Revealing mistake: One for swimmers to look for; when Bond is swimming beneath the ice near the ice palace you can see that he has a screw kick, but in the shots where you can see Pierce Brosnan's face you can see that behind him his legs are kicking correctly.
Continuity mistake: At the end of the Bond/Graves sword fight (after Miranda has stepped between them), in the close-up of Bond, he lowers his sword. In the long shot a fraction of a second later, it's raised in front of him again. (00:56:25)
Continuity mistake: When Gustav Graves arrives in his ice-slidey-vehicle, in the long shot the top starts to slide open, but in a closeup it's shut, and his assistant opens it. Plus he has the helmet in his hand when the glass lid is opened, but his head was so close to the top of the glass that there is no room for him to remove the helmet with the cockpit shut. (01:06:30)
Continuity mistake: At the end of the fencing battle between Graves and Bond, Graves has a nasty cut on his right cheek near his ear. When he and Bond meet again in Iceland the following weekend, his right side is shown close up and there is no sign of this despite only being a few days later. (00:56:33)
Continuity mistake: On the old subway platform when Q is about to introduce Bond to his "new transportation," they both look on as Q clicks a control to bring forth the carriage that has the still invisible Vanquish on it. The carriage almost passes them already when the shot cuts to another angle, and this time the carriage is still approaching on the railtrack from a bit farther away. Also, Q's right arm is now up holding the remote control, when in the previous shot just a second ago it was straight down by his side. (01:05:41)
Continuity mistake: At the end of the film as Bond and Jinx are in the helicopter after being dropped from the plane, as he is starting the engine, the caution/annunciator lights turn off 3 times in 3 different shots for no apparent reason whatsoever. (01:59:05)
Plot hole: Gustav Graves leaves Iceland in the Antonov 124 with Bond and Jinx actually watching the plane take off. Later the plane is seen in the middle of a military base in North Korea, where MI6 and the CIA cannot touch it. The flight from Iceland to North Korea would have taken at least 9 hours, during which it would overfly international waters and other countries. Surely it could have been intercepted and forced down before it reached North Korean airspace?
Factual error: After the window of the plane is shot out, the aircraft dips into a major dive which Jinx struggles to rectify. There's no reason this would happen simply due to decompression - that would be uncomfortable for the passengers but not affect the plane's flight characteristics.
Continuity mistake: When Bond uses his sound-ring to break the glass floor, we see the floor crack twice. (01:26:35)
Deliberate mistake: The cabin of a four-engined cargo aircraft such as the Antonov An-124 would not be whisper-quiet as it is portrayed in all scenes. Most of the plane's occupants would need to be talking in raised voices or even shouting to be heard.
Continuity mistake: When Bond is with Jinx at the beach in Cuba, he says to her, "It's when their prey comes out to drink." Jinx then takes the glass her from her mouth and brings it down the front of her body, but in the next shot she is drinking from the glass again.
Factual error: In the scene with the mining lasers, Mr.Kill positions a laser to be able to cut off Jinx's head. If you'll notice, the laser is still on and firing as he moves it. The way it spins down to get by Jinx, the trajectory would have already cut through Jinx. And even if not, it would have damaged the table she is on. However, when it cuts to the next shot showing the laser next to her head, there is no damage to the table, except to where the laser is directly contacting the table at that moment. No other damage is visible, despite it being on while being moved into position.
Plot hole: Bond and Jinx get on board the Antonov 124 by clambering on to one of the landing gear trucks. Bond gets on first and when Jinx climbs on in a shot from the inside of the landing gear well one can see from the background that the plane is moving at near takeoff speed - Jinx sure can run fast! Oh, and how did Bond and Jinx manage to run across the exhausts of the two right engines without getting blown head over heels?
Plot hole: According to Q, Bond's spy-car is essentially "invisible" thanks to tiny cameras on the perimeter that project what they see onto the sides. Except this in-movie explanation doesn't acknowledge the fact that the instant he'd start driving, dust, mud, snow and any other common debris would still build up on the outside and make it completely visible. Given that the movie takes place mainly in an arctic area filled with snow, there's no way the car is going to remain 100% clean all the time.
Visible crew/equipment: When Gustav is interviewed by a lot of journalists watch the window on the car and you'll notice a round screen used for lighting. In the opposite shots none of the press members holds one.
Chosen answer: Frost is proud of her martial skills and Sun Tzu's Art of War is considered to be one of the classic texts on warfare, but that's about as far as it goes.
Tailkinker ★