Factual error: When James Bond programs the two submarines to destroy each other we see the paths of the missiles displayed on a globe. They swing across in two arcs, narrowly missing each other. However, we are looking down on the surface of the globe, with no height perception, so the missiles should in fact travel in straight lines directly between the submarines.
Continuity mistake: In the scene where Stromberg is thanking Dr Bechman and Professor Marcovitz he he has a towel in his hand. When the camera changes to another angle that shows the back of his chair his hands are totally empty and resting on an arm of the chair. Then it changes back to the original camera angle and he now has a towel in his hands again.
Plot hole: When Bond's Lotus is being attacked while its traveling underwater it develops a few small leaks, which spray a thin stream of water into the car. When the Lotus drives out onto the beach, Bond rolls down the window and drops a big fish out of the car. How did that get in there? If there was a hole in the car the size of that fish, it would have flooded the driver's compartment and sunk the car.
Continuity mistake: When Q is showing the microfilm to Bond and XXX, Bond points at the Stromberg fish. But he points right at the projector. That would have made his finger much larger compared to the screen than it is in the next clip - and blurred. Furthermore the position of his finger on the screen doesn't match with the position he holds it in.
Other mistake: While Bond is being escorted by some guards, he opens a crate full of gas tanks, and begins fighting the guards off. If you look behind Bond in a brief scene you can see a few yards away another guard who is clearly watching this happening yet doing absolutely nothing.
Audio problem: After Bond sets the timer on the bomb at the end, the ticks don't add up. There's a definite tick each second, and you can count 12 of them after he starts it, then we cut back to the bomb and only 7 seconds have passed. (As a vague trivia aside, coincidence though it is, on the UK DVD he pulls the pin out at the DVD second timer ticks onto "07").
Factual error: At the end of the film Stromberg shoots at Bond under the table with a pneumatic spear gun-type weapon that shoots most likely a spear with an explosive tip through a long tube. This type of spear gun, unlike elastic-operated spear guns, has an actual sort-of gun barrel that's closed at the back. As such, when Bond shoots Stromberg through the tube with his hand gun, he somehow hits him, despite the fact that the bullets would ricochet off the closed barrel.
Revealing mistake: In both instances in the film where a helicopter explodes, it is quite evident that it is a model and it falls to the sea in one piece.
Revealing mistake: In the scene where the speedboat is landing onto the sea, after bursting out of the large tanker, one can see dummies on the speedboat.
Continuity mistake: When the rescue pod is speeding towards the surface you can see it has a keel weight which, judging from the size of the pod, must be 3-4 meters long. When it floats into the cargo bay of the navy ship, there wouldn't be room for the keel. You can see that the water level in the cargo bay is no more than 1-1½ meters.