Continuity mistake: When Disco Volante drops the stern and speeds away, the right ski, where Bond is supposed to hang on, is visible. But he's not there.
Continuity mistake: In the scene where Ursula Andress confronts Marcello Mastroianni, he reaches into an ice bucket where you see a very small pistol (PPK). When he points it at her, it changes into (I think) a Colt 45. It then, in another angle changes again into (I think) a Mauser Parabellum... Mistakes can be made if filming covers many days on the same scene, but when the dialogue mentions how he can hide a tiny pistol in the ice bucket.....
Continuity mistake: Near the beginning when Lee Van Cleef looks at the the wanted poster on the ticket booth at Tucumcari (just after getting off the train), there are two extra zero's drawn onto the poster (as added by the villain). Van Cleef then takes this poster away with him, and slots it under the door of a hotel room on a later scene - notice that the additional zero's have since disappeared from the same poster. (00:06:30 - 00:09:20)
Continuity mistake: Harry Palmer uses the leather wrist restraints to lacerate his wrists - the pain enables him to resist being involuntarily hypnotised. The next time he is woken roughly by the guards for another hypnosis session, his wrists are unmarked.
Continuity mistake: Lombard trips going up the stairs in the dark; he falls on his right side, but he waves the others to go up lying on the opposite side, facing the opposite way. (01:04:30)
Continuity mistake: James Garner figures out he's being duped, and tells Eva Marie Saint to run out of the room screaming to draw attention to herself. She does and there's a shot of her on the hospital lawn with staff all around her. The next shot is James Garner looking out the window to see what their reaction is, and Eva Marie Saint can be seen behind him in the room.
Continuity mistake: The streets and alleys are wet from a recent rain. Patty and Agent Kelso are following a cat. When Patty's boyfriend comes near, Patty lies on the ground next to a bush to avoid being seen. When she stands up, her clothes are completely dry.