Deliberate mistake: When 11 is dropped into the water and eaten by the piranha's, although the ravenous fish probably ate most of her and what was on her, there should at least be pieces of clothing that would rise to the surface in the flurry of activity. Not to mention that even though the water is a murky green all the blood from her body should have created a temporary, yet very noticeable darkening of the water.
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.
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?
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.
Revealing mistake: At the beginning of the film during Bond's "funeral", the shot cuts to a man watching the funeral from a boat through a pair of binoculars. The camera then moves to the newspaper next to him showing an "article" reporting Bond's murder. If you look closely at the "article" itself, you can see it was actually pasted onto the actual local newspaper. They probably bought a local newspaper and pasted the fake article over it to make it look authentic.
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.