Continuity mistake: When James Bond is fighting underwater with an opponent, the opponent rips off James' diving mask (which is blue). Then, James rips another mask off another opponent who is lying dead on the ocean floor. This dead opponent's mask is black. James puts on the black mask, and then he turns around, and the mask is blue again. (01:57:10)
Continuity mistake: Nicholas Hammond (Friedrich) was not a natural blond. The first scene to be shot involving him was the "My Favourite Things" scene and you can see that his hair is pale auburn. After this scene was shot, the directors thought that he would look better if his hair were lighter, so they applied an early form of bleaching agent to his hair. In scenes which were shot after this (notably the children's first entrance to meet Maria which occurs before the "Favourite Things" scene) his hair is very, VERY blond, almost white. In fact, if you scrutinise his hair closely throughout the film, it is a different colour in practically every scene, depending on when the scene was shot and how much of the bleaching agent had been applied.
Continuity mistake: Judge Cannon's magical handkerchief misbehaves right at the beginning of the dinner scene when he tries to make everyone else confess; it's not even in sight when he gets his tea, but pokes out a great deal when in close-up starts admitting his own guilt. (01:01:35)
Revealing mistake: In the final shot of the film the model makers neglected to include the antenna at the top of the Eiffel Tower, seen previously on the real tower in the establishing shot of Paris. (02:31:20 - 02:37:10)