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.
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?
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.
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: 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)
Plot hole: When Bond takes the short cut in the Q boat it jumps over a brick wall that leads to the end of the water where the London canoe club is based, meaning that the canoeists only have approx 50m of water to canoe in unless they scrape the canoes bottom away by going over the wall. Not much of a club, even for London!