Revealing mistake: When Bond escapes the Swiss bank through the window with the very large suitcase supposedly full of money (paper), he swings it around like it's empty (which it probably was).
Revealing mistake: When Bond is traveling to meet Elektra for the first time in Baku he sees a King helicopter cutting the trees. You can see that the person inside is a dummy.
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.
Audio problem: In the village in Azerbaijan, Bond tells Elektra she might be in danger and she laughs, telling him "I have something I want to show you" as she walks away in a long-shot. It's obvious this line was dubbed in during post-production - there's a very sudden, very noticeable drop in background noise and her mouth (although it's hard to tell from a distance) doesn't seem to move with the words.
Continuity mistake: When Bond first hits the water at the beginning of the Thames chase, the sky is very cloudy. A few shots later, in the overhead shot, it's blue skies and sunshine. (00:07:45)
Revealing mistake: In the mountains, when the two parahawks collide, they go at a certain speed but the shot later, they are only stuck together.
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.
Revealing mistake: Right at the beginning of the boat chase when Bond drives the boat through the waterway in MI6, before he jumps the boat into the river, there is a shot roughly from Q's POV, the boat clearly slows right down before it reaches the end. It couldn't fly as far through the air as shown.
Revealing mistake: Near the end of the movie where Renard and Bond are going at it, Bond is choking Renard and vice versa. You can clearly see Bond's thumbs aren't even touching Renard's neck.
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.
Factual error: When Bond's BMW gets cut in half it folds in on itself too much, as if the engine, axles, car interior, etc. has been removed. If anything the two halves should fall in the other direction.
Audio problem: The first line the banker says does not match his mouth.
Factual error: In the scene where Zukovsky is almost drowning in caviar he lies very deep - only the top of his face above the surface. The depth of a body in a liquid depends on the proportions between the density of the body and the liquid. For example in the Dead Sea, with its high salt content, the water has a high density, so a body floats higher than in fresh water. Caviar must have a quite high density too - probably as high as the water in the Dead Sea, since it tastes quite salt too. So if a person was floating in caviar, he would not go as deep down as Zukovsky does in that scene. That looks more like how deep he would go in fresh water.
Character mistake: After Bond and Christmas climb out of the blown pipeline (which is in Azerbaijan - since shortly before Bond was in Baku, and Electra was called and informed about a problem) Bond says "What are you doing here in Kazakhstan?"
Revealing 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.
Plot hole: When the hole is blown in the facade of the MI6 headquarter we first see flames and small debris - and then comes one more blast. Where did that come from? The money-bomb had already exploded and blown the hole in the building.
Visible crew/equipment: In the end of the boat chase, when Cigar Girl tries to shoot Bond, you can see that it's not Brosnan who is holding the rope; it's a stuntman.
Revealing mistake: During the chase in the mountains, the snow thrown up by bullet impacts is black rather than white, revealing their explosive origins.
Continuity mistake: When Bond shoots Renard in Kazakstan the bullet hits Renard's arm. Later when Renards is moving towards the elevator you can clearly see that his arm is undamaged.
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.
Answer: It's a variation on the "standard" James Bond theme.