Factual error: When the Russian capsule is launched, a palm tree can be seen - and it's doubtful that the Russian climate could accommodate palm trees.
Revealing mistake: When Blofeld destroys the volcano lair, as the camera is showing a view of the volcano, you can see the pressure waves move the bodies on the floor and tell that they are obviously dummies.
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?
Revealing mistake: When the helicopter with the magnet drops the villains' car into the ocean, look carefully and you can see that the car is empty.
Factual error: When Bird 1 is launched, both in the cave and outside, the exhaust plume and smoke trail is pitifully small compared to the plume of a real rocket.
Continuity mistake: During the car chase sequence, the radio antenna of the black sedan disappears and reappears between shots. It is most noticeable when the sedan is being lifted off. In the close-up as the magnet is attached to the car's roof, the antenna is visible. In the shots in which the car is shown from above, the antenna has completely disappeared.
Continuity mistake: When Hans picks up the table lamp to hit Bond, he picks it up by holding it close to the bulb. But when he brings it down to hit Bond, he is holding it the other way around. You can hear the bulb smash.
Deliberate mistake: During the scene involving Bond training at Tanaka's fighting grounds, right after Bond stabs the man with the blade at the end of a bamboo pole, no hint of blood can be seen on the blade, and yet the man's clothes are shown stained red.