Deliberate mistake: When Bond interferes with Goldfinger's cheating at cards in Miami Beach, we are watching the shot in which Goldfinger snaps his pencil and hits the table with his fist through binoculars from Bond's position far away on the hotel balcony. The sound of Goldfinger's actions are audible making the scene more effective. However, Bond and therefore the viewer wouldn't actually be able to hear it. (00:13:20)
Other mistake: Right at the end of the golf match when Bond is about to make his final shot, you can see two shadows being cast onto the lawn. Since the only source of light in this scene is supposed to be the sun, there should only be one shadow. The second one is caused by the set light. (00:29:35)
Audio problem: Whenever we're looking away from the bomb's countdown timer, it fails to advance as fast as it should, even though from time to time we do hear ticking at the same rate that the counter changes. For example, we see it tick from 010 to 009 and then hear 4 more ticks before it is stopped, but it then displays 007 and not 005.
Other mistake: In Fort Knox, where Bond has just gotten un-handcuffed from the bomb and is battling it out with Oddjob, Bond throws a gold bar quite a horizontal distance and hits Oddjob in the chest. The fact that it bounces off is in keeping with the fantasy of Oddjob's strength - but how in the world did Bond throw it that far? A Fort Knox gold bar weighs over 27 pounds.
Revealing mistake: Bond drives his Austin Martin into a wall because he believes that the headlights appearing before him belong to another car (actually, they were the reflection of his own lights). When he first sees the lights, they are directly in front of him, but only just before the crash, the angle of the reflection changes. And the way the mirror was hung up when Oddjob looks at it, it was in no position to reflect the light the way Bond sees them.
Plot hole: The planes spraying the gas are flying too high and too fast for the gas to be able to have any effect on the soldiers on the ground as quickly as it does. While we later find out that the soldiers were faking the effects, the too-rapid response should have raised the bad guys' suspicions.
Other mistake: When several cars are pursuing Bond and Ms. Masterson through the woods, the first car falls prey to the smoke screen. As the second car continues pursuit, a man leans out of its passenger window to shoot at Bond. But he doesn't appear to be aiming, or even holding his gun tightly; the muzzle waves far to one side for the first several shots.
Plot hole: Jill was sprayed with liquid or atomized gold. Yet there is no overspray anywhere, no paint on the bed or sheets, no dripping from Jill's arm to the carpet. Even if the paint was quick-dry, there would have been some paint residue just from Oddjob moving her around to spray her whole body.