Plot hole: In the final showdown, when Bond is fighting with Stamper, the girl is wrapped in a chain hanging from a crane and dropped in the sea. After the boat blows to bits, the chain continues to hang down even though there's nothing holding it. It even keeps hanging after Bond's swum down to untie her. What's keeping it there? Do all stealth battleships come with buoyant chains? With both arms at least partially free, why doesn't she just climb back up the chain?
Factual error: As Bond is preparing for the HALO skydive, he is warned that he has to freefall for 5 miles and without oxygen he will be asphyxiated. However, he jumps from a non-pressurised aircraft. Surely when the back hatch opened, the other people standing around would either also start to suffocate or be sucked out.
Revealing mistake: In the scene with the helicopter chasing them down the street, apart from the fact that the rotors should catch on something and hurl the machine into a wall, when it finally hits the wall at the end, the pilot and crew quite clearly become about 4 crash-test dummies. This wouldn't be so bad if it weren't for the fact that they are unpainted and all sit in their seats looking straight ahead with their hands in their laps while they are driven into a wall. You'd think they could have at least posed the arms over their faces or SOMETHING!
Deliberate mistake: In the helicopter and motorcycle chase scene, there are a few things that are not possible. A helicopter cannot hover at such a steep angle nor can it move slowly horizontally while being at that angle. A helicopter doing that at such low altitude will crash because it will tend to move in the direction the nose is pointing. Nothing in a helicopter can make it move in the way seen in this scene. Also, a helicopter cannot use its rotor blades as a cutting tool as seen in the beginning of this sequence. The moment the blades contact any object the helicopter will lose control and crash into the buildings in the sides. No room for error in such a narrow place and low altitude.
Continuity mistake: In Bond's hotel room, after Dr. Kauffman has killed Carver's wife, he takes out the tape that has been playing, holds it up, and it's fully rewound.
Continuity mistake: When James has just jumped out of the plane, he has a diving rig that is somewhat different to the one he has when diving on the wreck of the Devonshire. In the water he wears a twinset manifold air-bottle rig. While skydiving the rig was not manifolded and the bottles were in a different position on his back. To change between the two requires some work with a tool kit, preferably on dry land.
Continuity mistake: Gupta, Carver's gadget man, proves that Paris, Carver's wife, knows Bond extremely well by showing Carver some secret footage taken at the cable tv launch party. In that footage Paris says to Bond "Tell me James, do you still sleep with a gun under your pillow? As she asks him this question, Bond can be seen looking down over the railing at the crowd below. Yet if you rewind a few minutes to the actual moment in the movie when she asks him this question, Bond is not looking down, he is, in fact, regarding her fixedly. They clearly reshot it (even her intonation of the question is different).
Factual error: The helicopter, in the motorbike scene, does a strafing in a narrow road. That's absolutely impossible, as either some cloth would get clogged into the main rotor, or it would hit something and break. But that doesn't matter much, as the 'copter is going too slow to be tilted at that angle anyway.
Continuity mistake: The scene where there is a car chase with the very nicely equipped BMW, you could clearly see before the chase that the car was equipped with, I believe, five star rims, but in the scene it shows the back left tires having hubcaps instead of the five star rims.
Continuity mistake: As Bond is driving his BMW by remote control from the back seat, the bad guys shoot out the windshield with several machine guns and at least one rocket launcher. The damage to the interior of the BMW is substantial, most notably the bullet holes in the headrests in the rear seat. However, in a couple of subsequent shots the headrests are clean and undamaged, only to have the bullet holes suddenly re-appear in the following shots.
Continuity mistake: In the BMW chase scene the back window is clearly blown out, however as the camera goes back on Bond it is intact, and then missing as the rocket launcher goes cleanly through moments later.
Factual error: Both the Duke Class Frigates fire cruise missiles from the tubes. The tubes on the duke are purely for harpoon missiles and cannot be reloaded. Nothing in the missile room is actually used in the navy.
Plot hole: Why are Stamper's people filming the murders of the surviving sailors? If that footage is released, it would be strange, because the Chinese would of course never film killing British sailors. Furthermore the Chinese were only present in planes, and Carver is trying to make it look like it was the planes that sank the ship and killed the crew. How would the Chinese film the killing from planes?
Factual error: In the scene where HMS Devonshire is allegedly being sent off course because of spurious GPS signals, a brief space shot shows a CMGN communications satellite orbiting close to a GPS satellite. The CMGN satellite would need to be in geo-stationary orbit. The GPS satellites are in quite different polar orbits, much closer to earth. Moreover, GPS position-fixing requires data from several satellites, not just one. The alleged interference could not be made in this way.
Continuity mistake: Near the beginning when Bond causes mayhem, he sticks a grenade onto a moving vehicle and dives off it. As he jumps off and attacks a bad guy his collar is up (to better hide the face of the stuntman), then when it cuts back to a proper shot of him his collar's suddenly down.
Visible crew/equipment: In the scene when James Bond is trying to escape while driving his BMW from the back seat with a remote control, there is a 1-2 second shot where you can very clearly see a stunt man sitting in the front seat driving and then the shot returns to James in the back seat.
Continuity mistake: After Bond has disrobed Paris during their love scene, he puts his hands on her back and you can see that his left hand is on the top, but in the close-up of Paris in the next shot, it is now his right hand on top.