Factual error: When the air hose on the truck is severed, the brakes release. In reality, on an air-braking system, if the air hose is severed, the brakes lock on as a safety measure.
Deliberate mistake: Blofeld doesn't recognize James Bond in this film, even though they met face-to-face in the previous movie, "You Only Live Twice." There is a production-related reason for this. Ian Fleming wrote "On Her Majesty's Secret Service" in 1963 (in which Bond and Blofeld met for the first time), and he wrote "You Only Live Twice" in 1964. However, "You Only Live Twice" was adapted for film first (in 1967), and "On Her Majesty's Secret Service" was adapted afterward (in 1969). Because the 1969 film was so faithful to its source material, Blofeld and Bond are basically meeting for the first time... again. The producers were aware of this continuity problem and intended to have James Bond undergo plastic surgery for "On Her Majesty's Secret Service" (which would conveniently explain Blofeld not recognizing him, as well as the fact that Sean Connery had been replaced by George Lazenby in the lead role). But the plastic surgery idea was discarded in faithfulness to the novel, resulting in a glaring continuity problem between the 1967 and 1969 films.
Factual error: When M and his entourage arrive at Bond's estate, their cars are surrounded by sheep. They then drive on down an unsurfaced road to Bond's house, past a pride of lions he keeps on the grounds. A series of sweeping overhead shots shows us that it is all one huge field, with no fences or the like. Those sheep aren't going to last very long.
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 three 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.
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.
Factual error: When we first see Fatima Blush, she is waterskiing. She is doing several stunts, which are only possible with one ski, the most notable being skiing backwards with one foot in the air. However, when she releases the tow rope and skis up the ramp into James Bond's arms, she is on two skis. (00:45:55)