Continuity mistake: In the first scene, when Bond has a gun to the Swiss banker's head, in the first shot Bond's got his gun pressed right up to the guy's neck. However, when it cuts, the gun is a couple of inches from the banker's face. (00:02:20)
Continuity mistake: When Bond first hits the water at the beginning of the Thames chase, the sky is very cloudy. A few shots later, in the overhead shot, it's blue skies and sunshine. (00:07:45)
Continuity mistake: When James is chasing the other boat in the beginning, he fires the top torpedo first. Then, when they show him fire the second torpedo, the bottom hole is empty, and he fires the same torpedo (the one on top) again... (00:12:35)
Continuity mistake: At the end of the pursuit scene, the boat of the "cigar" girl stops on the bank of the Thames in front of the Millenium Dome. But it's completely in the water in one shot when Bond's boat passes over it, and it seems to be moored. (00:12:55)
Continuity mistake: When Q shows the boat to Bond, it looks much more damaged than at the end of the pursuit scene, when it landed relatively gently in water. (00:20:35)
Continuity mistake: When they're looking at the computer model of Renard's head (just after the doctor says "medulla oblongata"), count the pings. The first two times we hear one, a slight pause, then 3 close together, with corresponding green pointers on the image, then a higher pitched one on the green box. However, the third time (after "than any normal man") there's no initial ping with pause, just the 3 close together. Then just as we're expecting the higher one we cut to a shot of M, and we hear another middle beep before the final one. The sequence starts again, we cut back to the model in the middle of it, and we get an extra beep again, plus see that the beeps are now completely out of sync with bits of the model being illuminated. (00:25:50)
Continuity mistake: Just after Bond and Christmas Jones climb out of the pipe, Bond is holding his shoulder and his blazer sleeves are up. In the next shot, his arms are by his side and his blazer is all neat. (01:20:05)
Continuity mistake: When Valentin first falls into his Caviar it's very thick. In following shots the consistency changes to being much more watery. (01:30:35)
Continuity mistake: Just after Bond's BMW is sawn in half by the chopper, he says "Q's not gonna like this." In the close-up of him saying this, his hands (holding a gun) are not held up in front of his face. In the very next shot, viewed from behind, his hands are held high up and pointing towards the helicopter overhead. (01:32:02)
Continuity mistake: When Bond and Christmas surface, after escaping the submarine, there are no bubbles at all around them, which is impossible since we've just seen the submarine explode, releasing loads of gas. (01:57:10)
Continuity mistake: In the Caviar Factory scene, Bond is shooting at some enemies with a pistol. It cuts to a shot of Christmas and Valentin, then back to Bond. Now he has a submachine gun. Then, in another shot, he is back to his pistol again.
Continuity mistake: When Bond is sitting in the torture chair, and his right hand becomes free, you see him release his neck restraint, but never his left arm as he jumps from the chair.
Continuity mistake: During the speed boat and Bond boat chase in the beginning Bond's hair can be seen going from wet, to dry and neatly done, then back to wet a few times.
Continuity mistake: Right at the beginning of the film when Bond is trying to escape from the banker's office, he goes to the window and tucks his gun into his waistband. He then runs to the body lying on the other side of the office, and tucks it into his waistband again.
Suggested correction: This is incorrect. I've just watched the scene. Bond has his gun in his hand when looking out of the window and seeing police cars arriving. He then tucks it into his waistband to try to open the window. After the unseen sniper shoots the guard and Bond dives for cover, you can see his right arm pulling the gun out of his waistband, as he tries to work out where the sniper is. Then once he runs over to the dead body he tucks his gun back inside again. Not a mistake.
Continuity mistake: Pierce Brosnan's hair fluctuates in length noticeably throughout the film, most noticeably between walking down the path at King's funeral and moments later at the debrief at the MI6 Scottish Headquarters.
Continuity mistake: When Bond is with Electra, before he goes skiing (in the little room looking at the pipelines), he has at least one button done up on his jacket, then when he walks out to go skiing you see that they are all undone.
Continuity mistake: When Bond is under attack at the caviar factory the first time a bridge is blown up he falls backwards twice (in two different shots).
Continuity mistake: In the scene of the boat chase, Bond smashes the machine gun holder, and some parts fall on to the Cigar Girl. When the camera goes back to the girl there are no parts on her.
Continuity mistake: After the oil pipe is blown up, almost killing Bond, there's a large crater, as expected, but the blast also somehow severed the smoldering trees as if done by a chainsaw.
Continuity mistake: When M is imprisoned and is being spoken to by Robert Carlyle she is wearing a multi-coloured scarf which is draped over her left shoulder and down the left side of her body. When Carlyle leaves the room M turns around and walks towards the bed. The camera angle is reversed and she's not wearing the scarf. Later it is shown lying across the bed.