Revealing mistake: The shot of the two nuclear missiles being launched is used twice, just reversed. They seem to have changed the saturation slightly in one of them to make it look different, but there are identical clouds at the top left/top right in both shots, ruining the trick.
Continuity mistake: On the train, the wine stain on Jaws' jacket disappears for one shot and then reappears. It then changes size and shape repeatedly.
Plot hole: If they assembled the wet bike on the submarine, they wouldn't be able to get it off as it would be too big to fit through the hatch.
Plot hole: When Bond's Lotus is being attacked while it's 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 007 pushes Jaws outside the train, he breaks the window, but it is intact in the following shot. It's broken again a little bit later.
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 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.
Deliberate mistake: As the Lotus drives off the pier and enters the water, the exposed underbody is that of a normal car. After it enters the sea, the underbody we see is completely sealed, which it needs to be to allow the car to submerge.
Factual error: When Jaws kills the shark, the carcass floats on the surface of the water in the tank. It should sink to the bottom, as dead sharks do.
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.
Plot hole: When the submarine with Bond aboard sees the Liparus it is 6,200 yards away, and over to the side. How can it then suddenly be behind the submarine?
Continuity mistake: When Bond skis downhill in the beginning, in the close-up of his skis, you can see a hard, firm snow surface. But in the next clip, he is skiing off-piste.
Continuity mistake: When Shandor is about to fall off of the roof and is holding Bond's tie, his grip changes from very low - with about four inches left - to higher up, so he can slide down again.
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").
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.
Plot hole: Stromberg One is on 48 degrees West, Stromberg Two is at 22 degrees West, and the Liparus further east. That means that Stromberg Two has sailed at least 28 degrees since its departure from the Liparus. That is more than 2.500 km and would take a submarine several days. How did it get that far in a few hours?
Continuity mistake: When Stromberg is thanking Dr Bechman and Professor Marcovitz, the position and amount of food on his plate keeps changing all the time.
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.
Suggested correction: Maybe the ice bucket was always a part of the escape pod.
Ice that doesn't melt at room temperature - now there's an achievement.