Deliberate mistake: After Bond has killed the guard on the cliff, his final carabiner is shown sliding away. But the gravel it dislodges is falling noticeably faster than gravity would take it, indicating that the clip has been sped up for dramatic reasons.
Factual error: When Bond kills the guard who is trying to dislodge his pitons, the length that he fell would've left nothing but a big bloody mess. All he has is what looks like a few cuts and bruises.
Revealing mistake: When Bond attacks the ice hockey player in yellow with his stick during the fight at the hockey rink, you can see the player reacts to being hit just before the stick makes contact.
Factual error: The machine gun set up on the motorbike wouldn't work. The bullets wouldn't be able to be fired out of the indicator lights as the lights are too small and there is no firing mechanism fitted to them.
Character mistake: In the ice-hockey scene Bibi says: "They say that he is a defector from East Germany." That fits very poorly with the statement during the biathlon scene, where he is referred to as "The East German Champion".
Revealing mistake: When Locque kills Countess Lisl by running her over in his dune buggy, look in the cockpit and you can see that the driver is not Michael Gothard but his stunt double.
Continuity mistake: In the scene when Bond shoots Locque's car window and the car is hanging over the edge of the cliff, Locque puts his hand on the door when the car starts to fall, but in the next shot when Bond kicks the car over the cliff, his hand is no longer on the door.
Continuity mistake: When Bond is fighting the diver over the ATAC, Bond is holding onto it with his left hand. The diver then sends Bond crashing through a glass window, and when it cuts to the next shot, Bond is now holding onto the ATAC with his right hand.
Revealing mistake: Kristatos wants to run over Bond and Melina by boat, after he took the Atac. Bond and the girl swim to the sea floor, waiting till Kristatos is gone. You can see the (shadow of) the anchor hanging on the left side of the ship. But in the previous scene, you will notice the anchor is in the middle, on deck! And second: these kind of (speed)boats do not have an anchor attached below the water line, because it will reduce the speed. Conclusion: the underwater scene is fake.
Continuity mistake: When Bond is climbing up to the mountaintop fortress, he hammers in pitons as he goes up. But when he falls down, the three pitons are all level.