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.
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.
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 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)