Plot hole: Other than a reason to advance the the plot the Americans have no reason to launch their second rocket. If they're prepared to go to war because they think the Russians will steal another rocket then don't launch the rocket. It's not like there is an urgency to get another rocket into space so as far as the Americans are concerned what is the hurry?
Plot hole: If a fake burial at sea and a picture in the newspaper was enough to convince Bond's enemies that he was dead, was it really necessary to have him shot at in the bed at the beginning? We learn later that the girl he was with was part of the fake death (and probably the gunmen too) so couldn't Bond's people have just started with the newspaper and burial at sea to begin with rather than risking his life in the process?
Other mistake: When Blofeld blows up the crater at the end we see a shot of lava coming out of the top of the crater, but then we see a shot of the inside of the crater with all the bodies and barrels there is no lava. So where is the lava at the top of the crater coming from?
Plot hole: In order to stop the Spectre spacecraft, Bond dresses up as a Spectre astronaut and tries to sneak on board. But why didn't he just waylay all 3 Spectre astronauts, which would have scuttled the mission? Instead he just waylays 1 which allows the mission to continue.
Character mistake: While one of the Soviet mission controllers does speak with a native-sounding level of Russian, the other controllers and the cosmonauts sound obnoxious at times; strange anglicisms or outright English words are sprinkled into the script, such as the word "pressure" in the middle of an otherwise Russian sentence, not to mention the many grammatical errors.
Continuity mistake: When Bond is about to climb in the raft his hair is soaking wet and brushed forward. When he is inside it's nicely brushed to the right.
Revealing mistake: When the movie ends and Bond swims towards the raft together with the rest of the baddies, he is very obviously not Sean Connery but his stunt.
Revealing mistake: The volcano erupting is an obvious composite of at least two images: an explosion on a mountain and lava flowing. The cut-out footage of the lava is blatantly evident for one can see the outline of the pasted film, which has a lighter colour than the mountain's.
Revealing mistake: When the volcano erupts, the lava (a superimposed image) is flowing frame by frame as a stop-motion film as opposed to the explosion.
Continuity mistake: Bond grabs Kissy's both arms to help her climb inside the raft. Shot changes and he's just grabbing one arm.
Revealing mistake: When Bond starts flying the Nelly there's a close-up of him where a thick white outline appears around revealing his body has been cut-out and pasted on the flying footage. Problem is... his arm was erased. One might think it's an optical illusion caused by the visor but you can actually see the mountain right where his arm is supposed to be.
Revealing mistake: When the last helicopter explodes, in the close-up one can see it's empty.
Revealing mistake: When Bond destroys the two helicopters there are two thin wires above running along the screen, seemingly where they hung the scale models from.
Revealing mistake: You can see ropes lowering the rocket when landing.
Revealing mistake: Every time Bond is in the white Toyota, and they use a back screen projection look at the top of the windscreen, it has completely disappeared each side of the rear view mirror.
Revealing mistake: Look closely at the device Bond is using to open Osato's safe. Before he presses the button to reveal the individual number you can see what the number is going to be.
Continuity mistake: When Bond begins to make his way towards the rooms where the American and Russian astronauts are being held captive the announcer in the control room says interception will take place in two hours but then barely a minute or so later the announcer says "100 minutes." Somehow twenty minutes disappeared in just the time it took Bond to hide in the tram car.
