Audio problem: The first line the banker says does not match his mouth.
Factual error: At Valentin's Caviar factory, one of the lumbering choppers cuts through Bond's car. It is obvious that saw blades cutting through metal cause a high volume of sparks. Yet as the saws cut, the car is simply split in half down the middle, and falls apart. This would have ignited the gas tank, and the car would have exploded. Not to mention all the modifications Q has made to the car, with rockets and other explosive goodies.
Audio problem: In the scene where Reynard and his men are stealing the warhead, Bond jumps and dives through some blast doors as they are closing. While flying though the air, it is seen that he fires a shot. However, you never hear the blast. The flash of the barrel is easily seen, and it is obvious that he is not using a silencer from previous moments of that scene. He shoots, but you don't hear it.
Factual error: In the scene where Zukovsky is almost drowning in caviar he lies very deep - only the top of his face above the surface. The depth of a body in a liquid depends on the proportions between the density of the body and the liquid. For example in the Dead Sea, with its high salt content, the water has a high density, so a body floats higher than in fresh water. Caviar must have a quite high density too - probably as high as the water in the Dead Sea, since it tastes quite salt too. So if a person was floating in caviar, he would not go as deep down as Zukovsky does in that scene. That looks more like how deep he would go in fresh water.
Factual error: When the pipeline explodes it is clear during the explosion that it is mostly fire coming from the pipeline. There is no spray of earth or other debris. But afterwards Bond and Christmas are walking through a huge crater. Where (and when) did the earth get displaced, if it was not thrown up in the actual explosion?
Factual error: When the oil pipeline blows up we see 5 distinct explosions (coming from 3 different places) but there was only 1 bomb. Furthermore there is way to much fire for it to be a high-explosive detonation.
Other mistake: When Bond is about to jump from the banker's window, he is shown tying a knot on the strap, but when he gets to the street, he only releases the strap and walks away.
Suggested correction: He may have tied a quick release not, which by sliding his hand back up would have released the cable.
Bond does not tie a quick release knot. He ties a traditional overhand knot (it's shown in quite some detail), which cannot be easily removed. Therefore the original entry still stands.
Continuity mistake: When Bond has his gun pointed at Renard's head just before Christmas comes in at the bomb place, the gun is in the centre of Renard's head. Then the shot suddenly changes to a more zoomed out shot and the gun is pointed slightly to the left of Renard's head.
Continuity mistake: When Bond tells Renard that Elektra is dead, in the over-the-shoulder shot of Pierce Brosnan, you can see him making faces at Robert Carlyle (just before he starts screaming). However in the next shot of Bond's face, it's as if his face hasn't changed.
Suggested correction: The close-ups of Renard do not make it clear enough to see what Bond's expressions are.
You can see his face to the right of the screen mouthing something.
Continuity mistake: The gun that Elektra uses near the climax and which Bond takes from her is a Colt Mk IV Series 70. However, when he's on the submarine, it turns into a regular M1911A1. Compare the finish on the wood grips and the fact that the Series 70 has a stainless barrel, whereas the 1911 doesn't.
Suggested correction: There are a lot of bad guys on the submarine, it's entirely possible that Bond has killed one of them between shooting Electra and pulling the gun out again. chances are he may have even lost it when he dived to the sub.
I went back and checked this. The sequence of events after killing Elektra make a point of showing him tuck the gun in his trousers. He dives, swims to the submarine, and interrupts a sailor that is closing the hatch by kicking this man in the face and sneaking onboard. Literally the next shot after, a bald bad guy is walking down a corridor towards the camera and the gun comes into frame (held by Bond) and stops the bad guy in his tracks. Note the gun that is shown is drenched in water and it is the wrong gun from earlier at Elektra's. The hammer is not stainless steel and it is missing the gold insignia on the grip. You can even kind of make this detail out as the gun is shown still tucked in Bond's pants when he makes it down the ladder when entering the sub. It seems to already be the wrong gun. Besides the gun being covered in water, we just saw Bond kick a bad guy in the face and just a second after in the next shot he's holding up this second bad guy. To assume he needed to switch guns in between this very brief cut makes little sense when we just saw he had the gun tucked in his pants from Elektra's.
Factual error: Further to another submitted mistake, your sense of touch, which Renard is supposed to have lost, is largely made possible by the parietal lobe which is located at the top back area of the brain. Not only is the bullet in Renard's head shown to be nowhere near this section it's also nowhere near the stated medulla oblongata section which is at the bottom of the brain.
Revealing mistake: When Bond escapes the Swiss bank through the window with the very large suitcase supposedly full of money (paper), he swings it around like it's empty (which it probably was).
Revealing mistake: In the end of the boat chase, when Cigar Girl tries to shoot Bond, you can see that it's not Brosnan who is holding the rope; it's a stuntman.
Revealing mistake: When Bond is traveling to meet Elektra for the first time in Baku he sees a King helicopter cutting the trees. You can see that the person inside is a dummy.
Continuity mistake: In the nuclear decommissioning facility, when the Colonel, the soldier and Dr. Jones come down, the soldier hands the Colonel an AKS-74. However, when Renard shoves the picture of Dr. Arkov in the Colonel's chest, he doesn't have the AKS anymore, we can see he's not holding it because the Colonel holds the picture with two hands. After Renard grasps Bond's shoulder and walks back, he says "Without further interruptions" you can see another soldier holding the AKS-74. The Colonel is holding a Makarov when he orders the terrorists back to the surface.
Audio problem: In the village in Azerbaijan, Bond tells Elektra she might be in danger and she laughs, telling him "I have something I want to show you" as she walks away in a long-shot. It's obvious this line was dubbed in during post-production - there's a very sudden, very noticeable drop in background noise and her mouth (although it's hard to tell from a distance) doesn't seem to move with the words.
Revealing mistake: In the boat chase, Bond decides to dive below the barrier. It is very close to him, but takes about 5 seconds to dive. He would have hit it in about 2 seconds.
Revealing mistake: In the mountains, when the two parahawks collide, they go at a certain speed but the shot later, they are only stuck together.
Continuity mistake: In Zuckovsky's casino, the barman is not visible in one shot when James Bond is disarming the guard.
Continuity mistake: During the pursuit on the Thames, the Millennium Dome is near to the river but when Bond looks at the GPS screen, the building is not so close.
