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.
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.
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.
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.
Revealing mistake: During the action sequence on the labyrinthine docks on the Caspian Sea, one of the choppers with the rotating blades saws Bond's BMW in half. A cutaway shot reveals Bond nearby, murmuring, "Q's not gonna like this." The next shot is in back of Bond, seeing the newly split BMW fall apart, but Pierce Brosnan has been replaced with a dummy. This is most obvious during the over-the shoulder shot of the BMW falling apart, where Bond's gun is now held in front of him. Also, when the car splits in two, the dummy shakes a bit.