Visible crew/equipment: Watch for the boom when the cigar girl's Volvo boat swipes the building. It's on the top left of the screen on the widescreen version.
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.
Audio problem: When Bond arrives at the King Industries place, where he meets Elektra King, watch the man he talks to when he gets out of his car. It is painfully obvious that the man's mouth is not in sync with what he is saying. Even worse, the voice is not even his. It is slightly higher pitched than the man's real voice when he finally talks right.
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.
Factual error: In the final battle, Bond shoots up the dive controls of the submarine and it dives vertically down, straight into the bottom of the Bosporus. The sub is said to be a Victor-III that is about 100 meters long. The Bosporus around Istanbul, however, is only about 50 meters deep, so the rest of the sub would have stuck out of the water, not be fully submerged as shown.
Plot hole: In the Banker's Office, Bond takes the strap from one of the window blinds to facilitate his escape. Overlooking the large quantity of cable he ties round the belt of the villain and his own belt, there must be an awful lot of strap for one blind to allow him to drop from that high up to the ground (well over 50ft?).
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.
Revealing mistake: During the gun battle after Renard escapes the bunker, someone gets shot, and you see the stunt bloke dive to the floor and scream even though the gun wasn't even pointed at him or any bullets fired. He's the one standing just to the right of the jeep as we look at it.
Suggested correction: He's jumping out of the way, so he doesn't get run over by the jeep.
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.
Revealing mistake: When James Bond is on the run from the helicopter in the caviar factory, he backs into a metal pipe, holding his Walther P99 just above his head. Yet, if you watch the pipe you can see that it is a prop, as the pipe wobbles when Bond backs into it.
Factual error: King can't be a terribly good engineer. He's built his oil pipeline over a glacier. Glaciers flow. The pipeline would break within a year.
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.
Factual error: In the scene where James is being told why Robert Carlisle's character is so deadly (no pain etc.), they mention a specific part of the brain - Medulla Oblongata, which the character has a bullet travelling through. This is part of the brain is responsible for control of breathing and the heart - you can't survive a bullet there...
Factual error: In the scene where Bond is watching the screen showing the bomb going through the pipeline, he asks for the distance the bomb has to travel and how fast it is going. Bond is told the bomb "is 106 miles from the terminal, going 70 mph." Bond says, "We've got 78 minutes." Wrong. At 70 mph (1.17 miles a minute) it would take about 91 minutes to cover that distance.
Factual error: After the explosion in the pipeline Christmas says: "the world's greatest terrorist running around with 6 kilos of plutonium." That tells us that each half of the plutonium ball weighs 6 kg. Seconds earlier she asks "Why leave this half" and pulls out the other half of the plutonium from her bag. She lifts it with the tip of her fingers as if the container weighs no more than a pound. You can definitely not lift 6 kg with such a casual hand movement, and no significant weight change is visible in the bag.
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.
Factual error: When Christmas and Bond are on the rigs in the pipeline and are supposedly moving at about 70mph their hair only move about a little bit and very little flapping of the clothes. 70mph is a significant blast, try opening a window on a motorway.