Continuity mistake: In a scene towards the end of the movie where Bond and Vesper are lying on the beach, Bond has sand on his back through most of the scene. When they start to kiss, in the distant shot towards the end of the scene, he has no sand on his back at all.
Continuity mistake: When Bond enters his password in the casino, he enters 836547. He later gives the password as VESPER, which on an alpha-numeric keypad would be 837737.
Factual error: In the scenes at Miami airport you see numerous CSA planes (Czech Airlines). Czech Airlines offer no direct flights to Miami, however Prague airport, where this scene was shot, is full of CSA planes.
Revealing mistake: During the scene at the restaurant in Montenegro (actually filmed in the Czech Republic) you see a payphone with a Czech Telecom logo on it (itself a piece of history as these are all now rebranded O2).
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: During the chase at Miami airport the gas truck gets shot at and the rear tires blow. When Bond slides the truck to a halt the tires are fully inflated again.
Revealing mistake: When James Bond is supposedly in Montenegro, this was filmed in the Czech Republic - although they changed most of the signs they forgot some. When they are having a drink in the square there is a visible sign saying "Bily Kun" which means "White Horse" in Czech.
Revealing mistake: Near the end of the movie when Bond shoots Mr. White in the leg, you can see that Mr. White is wearing knee-pads under his pants.
Visible crew/equipment: In the scene where Bond is following the bomber in Miami Airport, when the bomber goes through the security door using the ellipsis password, and proceeds down the corridor,Bond tries to catch the door before it shuts. There is a hand visible which pulls the door shut for a brief second and holds the door in place.
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.
Factual error: When Bond retrieves the bombmakers's phone in Madagascar, he finds the Ellipsis message with a time code of 19:12. After tracing the origin of the message to the Ocean Club in the Bahamas, he finds the security footage of Demitrios sending the message at 19:12. But 19:12 is the local time for the Bahamas, as indicated on the surveillance tape and Demitrios' phone. Madagascar is 8 hours ahead, so the bombmaker's phone should have indicated the message was received at 3:12 a.m. Also, there is a lot of sunlight and activity going on for 3 in the morning.
Continuity mistake: During the scene in Miami at the Body World exhibit when Dimitri leaves the baggage tag for the second bomber the position of the baggage tag changes between shots.
Revealing mistake: When Bond is chasing the terrorist through the construction site, a large pile of black pipes fall from the building. While they are falling and as the hit the ground they make all kinds of metallic clanging sounds, but when they hit the ground, you can see that they are really plastic PVC pipes, as several of the pipe ends break off and small pieces fly off them.
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.
Factual error: When James Bond is swimming underwater, trying desperately to save the trapped Vesper, if you look, he is constantly yelling and exhaling, sending bubbles from his mouth. The problem is that this continues almost constantly for at least a full minute. Nobody has the sort of lung capacity that enables them to expel that much air and still function underwater for that long.