Revealing mistake: When Tee Hee and Bond are fighting in the train compartment, watch the right edge of the screen. In one of the shots the end of the set is visible as Bond shoves Tee Hee against the "wall", which wobbles. So much is revealed you can see the wooden framing.
Revealing mistake: As "Tee Hee" (the man with the claw) escorts Bond to the alligator pond at the farm, they at one point stand next to each other. You can see that Tee Hee's prosthetic arm is much longer than his real one- about as long as you might expect it to be, if the actor is really holding a prop with his actual (and perfectly good) hand.
Other mistake: When Bond is sky-surfing on the back of the other agent's boat, you can see a shadow above the skysurfer. Why would there be a shadow in the sky?
Revealing mistake: When Madeline Smith (The Italian agent credited as Beautiful Girl) emerges from the wardrobe / closet, she embraces Roger Moore. He then uses his magnetic Rolex to pull down the zipper on the back of her dress. If you look closely, you can see the cable/wire under dress pulling the zipper down. (00:11:20 - 00:12:00)
Continuity mistake: During the chase scene when several men in boats are chasing Bond in a boat, one of the bad guys steals a black speedboat from the Sheriff's brother-in-law. The bottom of the black speedboat collects white scuff marks as the chase continues, but the scuffs increase and decrease erratically, indicating that the sequences were not shot in the order we see in the film.
Continuity mistake: After Bond is picked up by the taxi at the airport in New York, Whisper in the "white pimpmobile", as Felix Leiter puts it, shoots the taxi driver in the head. The car then swerves from the second-left lane on the road to the very left lane. But in the next shot of Bond's head you can see through the rear window that there is a car on the left side of the taxi, indicating that the car is still in the second-left lane. In the next shot the taxi is back in the very left lane.
Revealing mistake: When Bond is giving Mrs Bell her flying lesson at the airport, the wings are torn off the plane. When Bond says, "Same time tomorrow, Mrs Bell?" the reaction shot of Mrs Bell shows the left wing to be intact. It is her same reaction shot when Bond climbed into the plane.