Randall's lunch in the paper bag disappears in one shot at the travel agency at the beginning of the film.
In the newspaper story about the smashing of the diamond smuggling ring, the first paragraph of the story is correct, but the second paragraph is about another story entirely.
When the ship's officer marches the boys off after their discovery as "stowaways", the camera pushes in and a moving shadow of the camera is visible on the wall to the left.
In the montage of London, Duke says, "Whaddaya know, London Bridge". What is actually shown is Westminster Bridge next to the Palace of Westminster (the Houses of Parliament) and Elizabeth Tower that houses Big Ben.