Continuity mistake: Just after Vesper has shocked James, the lead connecting the defibrillator to the chest pad can be seen to have come loose. When the camera cuts back to James, the lead has been reconnected. Note this is after the shock, not the disconnected lead that forms the drama.
Continuity mistake: When Bond is being tortured in the seatless wicker chair, in one shot when you look at the right side of Bond's face the blood is running in an unbroken line down his face. The next shot where you see his face the blood has been smudged, but in the next shot, where you see his right cheek, the blood is running unbroken again. This happens a few times in this scene.
Continuity mistake: At the Poker game between Bond and Dimitrios the chips change place during shots. Most noticeable on Dimitrios' small stack (two black chip stacks and one green) in the overhead shots they are on the black line of the table carpet, in the shots from the sides, they are in between two black lines. The same is with Dimitrios' cards and his good luck token.
Continuity mistake: At the end of the scene where Bond rolls the Aston Martin, during the wide shot just as the car finishes the last roll, the windshield is still on the car. In fact you can see the windshield fall back into a "normal" position. However, when the shot changes to the close-up of Bond in the car the windshield is no longer there.
Continuity mistake: When Carlos the bomber goes through the security door at Miami airport, he enters the door from a brightly lit area. We then cut to him emerging from the door - behind the door is completely dark. We then cut back to the door closing from the other side, showing that it's definitely intended to be the same door.
Continuity mistake: At the end where the building gets destroyed, in one of the shots on top of the destroyed building, Bond is looking at Vesper and her head is facing to the left. However in the very next shot and for a few more shots, her head is suddenly facing straight up at Bond.
Continuity mistake: After the torture scene, just after La Chiffre says he will feed Bond his "parts" you hear a scream from within the ship and then a gunshot. The camera shot then focuses on the ship's hatch. The handle on this door has changed from when the rest of the group went into the ship. The handle is now pointed to the right in the open position instead of straight up as it was when they locked the door. Just before "Mr. White" comes out of the hatch, you can hear the sound of the handle moving to the open position without any movement of the handle.
Continuity mistake: During the scene inside the sinking building in Venice, at 2:10:40, there is a shot of one of the floors collapsing. This allows debris, tools, ropes, rags, etc, to fall through the floor. 22 seconds later (2:11:02) they show another scene of a floor collapsing. This is the same event but has been shot from a different angle. If you look carefully, the same black rags can be seen getting hung up on one of the boards as the debris falls.
Continuity mistake: In the scene where James is giving Vesper CPR, the water is seen churning and bubbling through the skylight, and flowing over the roof but the building was no longer sinking at that point so the water would've settled. Also, everything around the building that sunk is perfectly dry.