Continuity mistake: The bomb is disarmed with 007 seconds left on the conveniently placed timer with big white numbers. Then, Bond says "Three more ticks and Mr. Goldfinger would've hit the jackpot." What? Well, originally, the timer would've stopped at 003, and the line would make sense, but later the powers that be decided to stop it at 007 instead for a good old Bond joke, and apparently never forgot to delete that line in editing. [The 3 clicks mistake is an interesting one as there are still in existence cuts of the film with the original 003 on the nuclear device timer. One contributor saw the 003 version in 1970 and was puzzled when the 007 version turned up on TV years later.]
Other mistake: The crushed 'cube' car is not the whole Lincoln; that kind of small cube is produced in junkyards from the body only, without wheels, drive train, etc.
Factual error: Goldfinger's disguised henchmen are dressed in Army uniforms, however, their rank insignia is Air Force.
Factual error: When Oddjob has the Lincoln crushed at the junkyard, it is smashed into a small rectangle, and dropped into the little falcon pickup. Even though the crushed car fits into the bed of the Falcon, it still weighs at least 2 tons. That weight would have dropped the back of the truck to the ground, but the truck doesn't even squat a few inches, let alone being able to handle that load with the tyres it has.
Factual error: When the Flying Circus is on it's way to Ft Knox, the lead pilot reports they are proceeding at 240 knots. Top speed on a Piper Cherokee 180 (the plane in question) is/was 141 knots.
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.
Factual error: It is impossible for Oddjob to have crushed the golf ball with his hand no matter how strong he is. For the way he crushed in his hand enclosed completly around it. It is impossible to crush even an egg that way unless you apply pressure all around. To his credit, Sean Connery wasn't blind to this. He repeatedly complained about this when he first read the script, that the golf ball scene was ridiculous.
Continuity mistake: After the game of golf between Goldfinger and Bond, Goldfinger gets Oddjob to show off his usually dangerous hat. He throws the hat at the statue and we see it fly off to the right of the screen, well away from the statue. Yet in the following shot, the decapitated head falls down next to the hat on the ground right by the statue.
Continuity mistake: You can see when the black Lincoln that Oddjob drives to the junkyard is lifted to be crushed, it has no engine or transmission.
Visible crew/equipment: During the scene at the golf club, when the Rolls Royce begins to move off, the reflection from one of the film set lights can be seen on the rear left hand side of the Rolls Royce: There is no way that this could have been the relection from the sun, because the weather during the scene was on the dull side.
Continuity mistake: When Oddjob drives away from the golf course, Goldfinger is not in the back of the car for some reason, even though they show him in the car earlier.
Revealing mistake: When Bond is on Goldfinger's plane - if you watch closely when it shows the external view of the plane in the sky you can see the plane is a model with two wires holding it up. The model plane's design and configuration are also quite different in mid-air.