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.
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.
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.
Continuity mistake: When Bond gets his X-ray glasses for the first time, he puts them on and looks down at R. In the next shot, his head is up again.
Continuity mistake: In the warehouse sequence Bond is taking cover from gun fire and yells to Zukovsky and Christmas "Get Out!" while holding his Walther P99. A helicopter cuts though the building his in and he drops down to protect himself (he's in the same place) and he's holding another gun (possibly an UZI) Then a couple of scenes later 007 drops down on two bad guys and shoots them with his P99.
Continuity mistake: When they're loading the submarine, and Renard is being kissed, from behind his lips are pushed forward, but when we see his face he's trying to pull back.
Continuity mistake: When Bond's in the chair having his neck broken, between two shots the handles change position. Also, at one point we hear that the woman turns the handles a bit, but in the next shot they haven't moved.
