Plot hole: The ferocious battle in the crater ends instantly when Bond blows up the space ship. Why? Aren't Blofeld's men still going to try to defend themselves? How do they know Bond has succeeded in his mission? They can't see the control room, let alone the television sets.
Plot hole: Blofeld tells the bad guys that they had Bond and let him get away. The woman says "but Bond is dead. It was in all the papers." As we saw in a paper near the start, there was a well publicised photo of Bond, and when she met him he wasn't using any kind of disguise, so how did she not recognise him if she'd seen the papers?
Plot hole: Right after Bond escapes Blofeld and joins Tanaka and Kissy, they say they need to get to the Control Room (that Bond just left from), they look at the "front door" to the Control Room and Tanaka says "Impossible! It's too well defended!". Why did they not go back the way Bond just came from, through Blofeld's "apartment"? Instead, they fight their way across the entire launching complex and go through another entrance, which ALSO leads through Blofeld's "apartment".
Plot hole: In the volcano base, Bond finds and frees three captured astronauts - two Russians and an American. But when they enter the SPECTRE astronauts' room, there are only two of them with Bond (and there is no indication that the third one was seriously hurt in the previous struggle with the guards); and after Bond is dressed in the spacesuit, they disappear from the story altogether.
Plot hole: At the end, we see pictures of the space shuttle several times on a TV screen. Where is the camera to film that?
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.
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?
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?