Continuity mistake: In the scene where the doctor is telling the staff of MI6 about Renard, she says the bullet is moving through the medulla oblongata which is located in the neck below the left ear. However, Renard was shot in the head above his eyebrow, and in the hologram, it shows the bullet was moving straight into the middle of his brain.
Character mistake: Why is Electra using Windows 2000 (still in beta at the time) to survey her oil empire? (I think it's just after she's asked M to come and help her) You shouldn't use beta software for anything important....
Revealing mistake: In the scene at the end when the sub explodes, you see the hull split in two and the propeller drops away. But you do not see the prop shaft.
Factual error: When Bond is in the little boat and nosedives it underwater to avoid whatever it was he was avoiding, he appears to be travelling at fairly high speed. With no windshield (or such a small one), the force of the water hitting him in the face should have knocked his head off or at least broken his neck.
Continuity mistake: When the pipe blows up, why does it blow up in three sections at the same time? Also, I might be wrong, but when we see the explosion it looks like a straight section of pipe, but when Bond and Jones are walking around afterwards, it's clearly a curved section that blew up.
Continuity mistake: Throughout the whole boat scene, Bond's little speedboat has a roof on it, but, when he goes up the ramp to jump onto the hot air balloon, the roof is gone so he can jump out. When did it come off?
Revealing mistake: When Bond goes skiing with Electra to check the pipe lines, in one scene you can see ski tracks in front of the pair. They could be from previous line inspections, but surely they would have been snowed over? That area doesn't look like a popular ski resort....
Continuity mistake: In the scene where Bond has the X-ray specs he looks at a man who has a pistol and a knife in his pockets to the left, and over his right shoulder is a semi-automatic pistol. He confronts the man and both the knife and pistol are taken out, but the semi isn't seen again.
Visible crew/equipment: In the scene where Bond is at the caviar factory at one point he takes a tumble down a set of wooden stairs. As Bond falls down the stairs we see the actor's face and it is obviously a stunt double.
Factual error: During the boat chase, the part when Bond jumps the boat through London Canoeing Club shed was filmed in the canal at Tobacco Wharf in London. This is not actually the home of the L.C.C. Across from this in real life is a road and then a dead end yet once Bond hits the road he finds himself in what appears to be Camden Fish market!