At the travel agency, the globe rotates between shots. At first it shows the Americas; later it's rotated so only the Pacific Ocean is visible.
Despite being advertised as a "monkey" at the pet shop and referred to that way later in the film, Dickie is really a chimpanzee.
When Louise is hitting her father in the face with the chocolate cake, there is a mirror behind them. In the mirror you can clearly see the cameraman's legs - he's wearing white tube socks and dark shorts.
In the scene where Louise pushes her father, played by Ray Milland down the hill, you can see that Milland's stunt double looks nothing like him. He is a man with brown hair and a beard, when Milland was completely bald in the film.