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.