Factual error: Carver's ship would not be even close to stealthy. Every angle and crevice on it, while cool looking, would be a beacon for radar. Nothing stands out on radar more than a right angle. A picture of the real stealth ship can be found here. http://www.fas.org/man/dod-101/sys/ship/sea_shadow.htm
Continuity mistake: There is a shot from behind a video camera, showing a wire or cable coming out of the back of the video camera, however, in all subsequent shots the wire/cable is not present. (00:00:50)
Continuity mistake: Bond takes a watch from Wai Lin's computer-weapons room. The watch is shown to be an Omega Seamaster, the exact same model worn by Bond earlier in the film, but with a few improvements made by Wai Lin's organization, according to her. This model of watch is equipped with a helium escape valve, a knob located on the perimeter of the case at the 10:00 O'clock postion. The close-up of the watch shows this. Later, Bond removes a small remote-controlled detonator from the watch which has the helium escape valve control knob attached to it. The close-up insert shot shows that the knob is no longer attached to the watch at the 10:00 O'clock position, and the close-up shot of the rigged grenade-in-a-jar bomb shows the control knob as a part of the detonator. When Bond and Stamper have their final show-down at the end of the film, there are many shots showing Bond's watch and the helium escape valve control knob is inexplicably back in place on his watch.
Visible crew/equipment: When Bond and the Chinese agent are being chased by the bad guy's helicopter across the roof tops of Shanghai, the film crew's helicopter can be seen towards the top right hand side of the screen when the camera cuts to the front view of Bond on the motorbike. The next shot of the chase is then filmed from this helicopter.
Continuity mistake: When Bond parks the BMW, the tyres are turned slightly to one side. When the bad guys come to break into it, they're perfectly aligned with the body of the car.
Audio problem: In the scene where James Bond and Wai Lin are introduced to Mr. Carver and Mr. Stamper, Carver says that when Stamper removes Bond's heart, " there should be just enough time for him to watch it stop beating". While saying this, he turns to walk towards his desk and his lips don't move at all. His quote was obviously added in post-production.
Continuity mistake: James and M are travelling in the motorcade. The privacy barrier is lowered to reveal that Moneypenny is in the front-passenger seat. The shot changes to an exterior shot of the limousine. You can clearly see the privacy divider rising during this shot. The shot returns to the interior of the limousine for more dialog. Then the shot returns to Moneypenny for her to say that James will have to decide how much "Pumping" is required. Once again you can see the privacy divider rise. (00:26:59)
Other mistake: When Carver is typing Bond's obituary on the big screen, he hits many more keys than would be necessary to write the end of the sentence.
Continuity mistake: In the scene where James is trying to escape from Carver's headquarters, a black guy holds him over the newspapers being printed. In one shot the back part of his tie (that hides behind the larger front part usually) is hanging by his ears, it cuts to a shot of the black guy and when it cuts back, the back part of the tie has risen back to its proper place against his chest.
Factual error: A Type 23 Duke Class Frigate is used as 'flagship' for the fleet at the end of the film. The Type 23 is way too small and undermanned to act in such a capacity; it has no command and control facilities. They should have used at least a Type 22 Batch 3 Frigate, a carrier or an LPD (Landing Ship). We also see the evidence of a fleet on their radar screen, but nothing more of them.
Deliberate mistake: This mistake/trick was revealed in the second DVD commentary on the film. When Bond is underwater in the ship with the flare, this flare does not behave realistically. If they had used real flares, it would have put too much smoke and dirt in the water and quickly made it too murky to see or film through. So the flare used was a special effects prop of a bright light with bubbles being fed through it to give a good effect, but is not how a real flare would be under water. (01:08:25)
Continuity mistake: When Carver has Bond and Wai Lin in his new building after capture, he is writing their obituaries as he narrates it. The camera zooms slowly closer to Bond and Lin before cutting to a close up of Lin. Suddenly, her mouth is shut when it was partly open before, and her hair is in a slightly different position. (01:13:34)
Continuity mistake: The scene where Carver is writing the newspaper headline, he changes it from "British sailors killed" to "British sailors murdered." The camera then cuts to a close up of his face, and reflected in his glasses we see the other page (with the headline in different languages). The top text box changes so it has two rows of text. However, when the camera cuts back as Stamper calls in, there is mysteriously only one line of text again.
Factual error: In the Oxford scene, Bond is in bed with the Danish professor in the New Buildings wing of New College. The problem is that all the rooms in the New Buildings are student rooms and have always been so since they were built - no professors live or teach in this building. The professors are on the other side of college.