Continuity mistake: When Bond escapes from the Willard Whyte facility in the desert in the moon buggy, a car that is chasing him goes over a ridge and turns on its side as the buggy speeds by. A wheel rolls back into the shot, all on its own. It doesn't belong to the car, or the three three wheelers also chasing, but looks like it belongs to the buggy, which has its full compliment of wheels all through the scene.
Continuity mistake: The famous car chase ends with Bond's car tipping up on its right wheels to fit through a pedestrian path. However, when it emerges the other side, it's tipped on its left wheels. [When the car enters the alley this was filmed in a studio. When the car exits the alley this was filmed in Vegas. The first few times the exit was filmed the car emerged on the correct wheels but the shots were unusable because of the crowds in the background watching the filming. This shot was temporarily abandoned and eventually re-filmed with a different stunt driver who famously performed the stunt on the wrong wheels. Realising this, the producers filmed an insert shot featuring a close-up of Sean Connery and Jill St John which shows the car tip back onto four wheels and then up onto the opposite two wheels (even though the alleyway would be too narrow to manage this!), which is in the finished film].
Revealing mistake: Bond escapes from the buried pipeline when two technicians open a hatch from the outside. One tech unlocks the hatch by rotating a large wheel which drives the locking mechanism. But when he finally opens the hatch, there's absolutely no mechanism attached. There's just a bare axle that the wheel turns on.
Revealing mistake: When Bond escapes from the research facility, guards give chase on three-wheeled vehicles. One of the guards goes off an embankment & wipes out. He sets the vehicle up and prepares to drive off. Bond is supposed to run up, kick the guard off & take the vehicle. Connery is so slow in this scene that the stuntman has to sit on the vehicle & wait for him to run up for the kick.
Factual error: While Bond and Franks are fighting in the lift you can hear glass breaking, but when Franks picks up a shard of it to stab Bond you can see it's really a piece of Plexiglass. When Franks is forced to let go of the shard his hand shows no cuts or blood, which would have been unavoidable the way he had been holding it.
Revealing mistake: When Bond is in the trunk of the car, being taken out of the lower level of the Whyte House, a trap door opens out into the desert. The car however does not emerge from the door, which is never seen, but appears to be simply driving along a road. The 'door' is apparently a silhouette cutout raised in front of the passing car.
Revealing mistake: On the oil rig, when Bond tells Tiffany to "shoot 'em" after she gets the gun, three bad guys run towards her. A helicopter drops a bomb in front of them, taking them out, but watch the guy who is the furthest away. The bomb lands a good 20 feet away from him, far enough away not to do any harm. But he crouches a little and stays up, then he looks at his other two crewman a bit puzzled, and then falls down a bit later as he finally realises what he was supposed to do.
Factual error: In Blofeld's offshore control room there's an Earth-globe turning under a model of the satellite, to illustrate its orbital groundtrack. The way it's arranged, however, shows an orbit which is impossible. It shows the satellite tracing a groundtrack over a constant latitude. The only instance in which this is possible is if the orbit is directly over the Equator, whereas the model shows it over a latitude well within the Northern Hemisphere.