Continuity mistake: In the opening, Bond finds the button to let open the secret hatch in the oil tank. This hatch looks very heavy and is driven by a motor or something; you can hear the humming sound of it as well. When Bond is inside, now he can close it by hand. Also when he leaves the oil tank, he uses the same hatch, and can now open and close the hatch again with his hands.
Continuity mistake: When Bond first sees golden Jill on the bed she is lying diagonally across the bed with her right foot on the bed and pointed like a ballerina on points. As Bond approaches the bed her right foot is pointing towards the camera. The last shot of Jill's legs show both her feet hanging over the end of the bed meaning that she has changed position and is now lying straight along the bed.
Continuity mistake: Goldfinger's crew uses a giant truck-mounted laser to burn their way through the Fort Knox entrance. Several shots of the truck show the laser beam being moved across the entrance extremely rapidly; however, when these shots are intercut with views of the entrance itself, the beam inches across the entrance door very, very slowly.
Continuity mistake: At the Miami resort, when Goldfinger walks towards the card table, on the far left you can see Bond and Leiter standing watching Goldfinger in the background. In a close up shot of Bond and Leiter we see Bond reaching for a towel and putting it on his shoulder, but then in the wide shots there is no towel over his shoulder and he never moves.
Other mistake: When Q briefs Bond about the Aston Martin, he tells him the homer (tracker) has a range of 150 miles. When Bond is tracking Goldfinger in Switzerland, he is momentarily distracted while Tilly overtakes him. The blip on the screen has then disappeared, meaning G's car is some 150 miles ahead. But moments later, Bond pulls up on the hillside above where G has stopped for refreshments. How could he have made up the best part of 150 miles in so short a time?
Plot hole: As Goldfinger points out there are 41,000 troops stationed at Fort Knox so how in the world was Goldfinger able to make his escape? The troops should have easily been able to overpower Goldfinger's men without much of a fight and certainly shouldn't have been so easy for Goldfinger himself to get away on the helicopter.
Continuity mistake: Bond is in bed with Jill. He goes to get some ice and she faces forward at him. A shot later she is facing upwards and her head is tilted sideways.
Continuity mistake: When Oddjob throws his steel-rimmed hat to kill Tilly, you can see the hat falling in a downwards direction, yet it still manages to hit Tilly on her neck.
Other mistake: In the scene where the flying circus pilots are introduced and are landing, you can plainly see that one of the pilots is a man with a cowboy hat on, rather than one of the girls.
Plot hole: When Bond goes into the kitchen for the champagne, Oddjob is waiting for him. But where was he hiding? Oddjob couldn't have hidden in the bedroom without being seen. The kitchen is separated from the bedroom about halfway by a metal grate and not a wall. Oddjob could have only been hiding in front of the cupboards since we can see Bond from the bedroom POV all the way to the refrigerator. There is no possible way Bond wouldn't have seen him or even brushed against him. There is lighting in the kitchen, which we know because Bond is illuminated when he walks in; he casts a strong shadow on the floor during and after his fall (not from the refrigerator); and is illuminated when he stumbles out. The pan shots of the kitchen show no places where Oddjob could have concealed himself - and he is not exactly on the thin side.