Deliberate mistake: The famous car chase ends with Bond's car tipping up on its right wheels to fit through a pedestrian path. However, when it emerges the other side, it's tipped on its left wheels. When the car enters the alley this was filmed in a studio. When the car exits the alley this was filmed in Vegas. The first few times the exit was filmed the car emerged on the correct wheels but the shots were unusable because of the crowds in the background watching the filming. This shot was temporarily abandoned and eventually re-filmed with a different stunt driver who famously performed the stunt on the wrong wheels. Realising this, the producers filmed a somewhat clunky insert shot featuring a close-up of Sean Connery and Jill St John which shows the car tip back onto four wheels and then up onto the opposite two wheels, even though the alleyway would be too narrow to manage this.
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Service" (which would conveniently explain Blofeld not recognizing him, as well as the fact that Sean Connery had been replaced by George Lazenby in the lead role).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.
Deliberate mistake: When Bond is fighting Zhao in the clinic, they accidentally set off the tomograph Zhao was lying in. As this machine's powerful magnetic fields indeed would pull any metallic object in, no doctor with common sense would allow sharp objects and other stuff within range. You aren't even allowed to carry watches and have to report any dental fillings. (00:43:50)
Deliberate mistake: On the roof of the sunken building, Bond tries CPR on Vesper, then quits when he realizes that she is dead and sits away from her body. Watch her right leg carefully when he returns to her body and cradles her in his arms - she flexes it upwards at the knee. Yes, I know that electrical impulses in a dead body can cause muscle movements, but this was obviously the actress involuntarily bracing herself from slipping on the slanted surface. Cut to Mr. White walking away with the money and when the camera returns to the roof, Vesper's leg is lying flat again. (02:18:00)
Deliberate mistake: When we first encounter Tilly Masterson, she overtakes Bond and he decides not to pursue her. Then, when Goldfinger has stopped, Bond is actually ahead of her as she nearly hits him with a rifle shot. Given that most Swiss passes are single carriageways, surely Bond would have noticed her had she parked earlier. (00:33:30)
Deliberate mistake: When 11 is dropped into the water and eaten by the piranhas, 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, but very noticeable darkening of the water.
Deliberate mistake: Throughout the entire movie every character seems to speak fluent English, despite several portions of the movie take place in remote Russian locations.
Deliberate mistake: In the scene inside the belly dancer's dressing room, during the brawl Bond has with the KGB agents, he shoves the bald headed guy into the mirror along the bottom 1/3rd of the glass, yet the middle along the left hand side of the mirror makes it look as if that was the initial point of impact before it shatters.
Deliberate mistake: This mistake/trick was revealed in the second DVD commentary on the film. When Bond is underwater in the ship with the flare, this flare does not behave realistically. If they had used real flares, it would have put too much smoke and dirt in the water and quickly made it too murky to see or film through. So the flare used was a special effects prop of a bright light with bubbles being fed through it to give a good effect, but is not how a real flare would be under water. (01:08:25)