Continuity mistake: During the car chase, Bond jumps into his car through a right hand side window. In one shot the front window is open, the camera changes to Bond. Then we see the back window is open and the front is closed. Bond jumps through the back window.
Continuity mistake: During the remote-control BMW car chase scene, there are a couple of clear shots of the steering wheel of the BMW shown not moving at all as the BMW is making violent turns, demonstrating that the steering wheel itself is not a part of the remote steering mechanisim within this particular vehicle. However, subsequent shots show the steering wheel spinning wildly in either direction as the car is going through its paces during the rest of the chase.
Continuity mistake: When James breaks into the lab on the roof, he replaces his phone in his inside left jacket pocket. When he goes to fry the security lock on the office door, he pulls it from his inside right jacket pocket.
Continuity mistake: In the scene where Bond is driving to his hotel room to find Paris dead, throughout several shots, the car window rolls itself up and down.
Visible crew/equipment: James hurls a Heavy in a red jacket into a printing press; as he breaks the paper, you can just make out a black crash mat.
Revealing mistake: When Bond holds Carver against the computer so the big drill will kill him, you can easily see that the computer behind them isn't real. As the drill rips into the 'computer' it's all white inside, just like styrofoam. They probably used it as it gets destroyed easily and would make the drill look really powerful as bits of it flew everywhere.
Continuity mistake: When Bond knocks out the MiG's copilot with the helmet, in the shot from behind the pilot (where Bond is quite obviously Pierce Brosnan) he is seen with a Beretta 92FS. However in the shot from behind Bond (now stuntman Wayne Michaels), the gun the copilot drops is now a Browning BDA. (00:05:30)
Continuity mistake: The Chinese agent handcuffs Bond to the shower. Then she is running away and you can see her from the back picking up a piece of clothing. Her hair is completely dry, although she was under the shower with Bond only a few seconds ago.
Visible crew/equipment: When the BMW shoots the car with its car rocket launcher, the rocket then hits the car, sending it flying back, you are able to see a set of wires leading under the car then off screen.
Audio problem: After the engines of the stealth boat are stopped, Bond is walking around with a sub machine gun and his pistol. His pistol has a large silencer/suppressor on it. A man tries to ambush him on a later and Bond turns and fires his pistol at him several times. Despite the suppressor, the gun makes the full sound of the shots. (01:45:14)
Factual error: In the scene with Bond in Oxford, the audience sees an aerial shot of the college he is supposedly studying Danish in. The college shown is Brasenose. However, in the next shot showing the college courtyard, the college has magically switched to New College - 10 minutes' walk from Brasenose.
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.
Factual error: Carver tells Stamper to be sure and use the correct ammunition when shooting the British sailors. Stamper then uses an M60E3, an American light machine gun firing 7.62x51 mm ammo. To properly frame the Chinese, he should have used a weapon firing 7.62x54R mm, 7.62x39 mm or 5.45x39 mm ammo.
Plot hole: One of the most memorable aspects of this movie is the motorcycle/helicopter chase scene. There are machine guns firing hundreds of rounds, there's a motorcycle leaping from rooftop to rooftop, and a large helicopter performing some amazing aerial stunts, then eventually crashing. All of these things happen in a very crowded part of the city. Yet after the crash, Bond and Wei Lin walk from the courtyard area where most of the action has taken place to the street just on the other side of the buildings, and no one seems to have noticed gunfire, the exploding helicopter, etc.
Continuity mistake: In the car chase in Hamburg, when Bond is in the back seat remotely driving the car, the car does a U-turn into another lane. After the car says "Reduce speed - pedestrians in roadway" there is a shot of the car's dashboard from inside the car, with the car travelling straight forward. The steering wheel, however, is tilted to the right, even though 1) The car is travelling straight and 2) The car had just made a LEFT turn. (00:57:30)
Continuity mistake: In the scene where the ship is being confronted by the Chinese MiGs and is attacked by the stealth boat an alarm sounds on the ship and all the sailors in the mess hall leave and go to their battle stations. A few shots later when the drill hits the ship and water rushes in it shows three or four sailors in the mess hall getting hit by the rushing water.
Factual error: To know this you have to live in Hamburg, Germany : The hotel park deck Bond's BMW is chased on is on the left side of the big shopping street. But his jump across this street is from the right to the left. (01:00:35)