Visible crew/equipment: When 007 takes the taxi outside the Oh Voodoo Cult Shop, you can see the reflection of the crew on the window of the car.
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.
Factual error: Although it's already been mentioned that the scene of the shuttle being stolen from the back of the 747 is impossible because the shuttle wouldn't be fueled while being transported, it should also be noted that even if the shuttle was fueled, it would still be just as impossible: During the getaway, the thieves ignited the shuttle's 3 main engines to get free of the 747 and escape: the thing is, the shuttle's main engines are fueled entirely by the large external tank the shuttle and the solid fuel boosters are attached to during liftoff, and once the tank is jettisoned, these engines cannot be used. The only engines the shuttle's internal fuel feeds are the reaction control thrusters, and the Orbital Maneuvering System (which are the two smaller engines located in the bulges just above the main engines). Both the RCS thrusters and OMS engines are almost totally useless within the atmosphere, so even if the thieves managed to get the shuttle free of the 747, they could only get it as far as it would glide unpowered: In fact, they could probably get it further if it wasn't fueled. It should be noted that this is not a fictional, futuristic spacecraft: It's a bog standard shuttle, stolen from NASA, on the back of the modified 747 used by them to transport the orbiter from its landing site to Cape Canaveral.
Continuity mistake: After Pola Ivanova sneaks out of the baths, she climbs into the car with General Gogol, who can be seen to be a double and not Walter Gotell. (01:07:20)
Other mistake: On the prison computer scan of Ernst Stavro Blofeld, Blofeld's date of birth is shown as 4th July 1946, but he is only meant to be a few years older than James Bond, as seen in the photo of them together as teenagers in the film Spectre. That photo is meant to be circa 1985, and the newspaper clipping (also shown in Spectre) about Franz Oberhauser's (aka Blofeld) death in the avalanche happened when he was 16 years old. If he was 16 in 1985 then he should have been born in 1969, not 1946.