Orson Welles was a little upset he did not get a cameo in the film. He was upset because before Michael Todd produced this film, he produced a stage version by Welles. The play flopped but Todd turned the project into a film anyway and it enjoyed great success. Welles felt he gave the idea to Todd in the first place.
At the beginning of the movie when Passepartout is on his way to the employment agency on the high-wheel bicycle, a white horse comes up beside him and even next to him, but in the next shot, there is no horse anywhere nearby.
When the tall ship US Grant arrives in San Francisco, you can see the radar installations on the mast which did not exist in 1872. The vessel is a stock shot of the contemporary 1950s Japanese training ship 'Nippon Maru'.
After arriving back in England it was discovered that they returned a day earlier than they expected because they crossed the International Date Line west to east and therefore gained a day. The date line is in the middle of the Pacific Ocean and they would have had many opportunities to learn the correct date before arriving in England. In fact, they had to know the correct date in order to cross the U.S. and sail across the Atlantic Ocean.