When negotiations over his film The Sand Pebbles kept breaking down, Robert Wise started looking around for another project to do while he waited for things to get sorted. The Sound of Music basically fell into his lap after William Wyler dropped out of the project. Wyler wanted the film to be more serious and make more of the Nazis in the story. 20th Century Fox didn't care for his approach.
When setting up for filming the Captain and Maria's wedding scene, there was nobody at the altar to wed them when they reached the top of the stairs. Someone had forgotten to summon the actor playing the bishop. According to Julie Andrews, the real bishop of Salzburg is seen in the movie.
When the Best Picture Oscar went to The Sound of Music (April 18, 1966), it was the first time the Academy Awards had ever been broadcast in color (ABC TV) (see also The Greatest Show on Earth).
When the film was released in South Korea, it did so much business that some theaters were showing it four and five times a day. One theater owner in Seoul tried to figure out a way to be able to show it even more often, in order to bring in more customers. So he cut out all the musical numbers.
While the von Trapp family hiked over the Alps to Switzerland in the movie, in reality they walked to the local train station and boarded the next train to Italy. From Italy, they fled to London and ultimately the USA. Salzburg is in fact only a few miles away from the Austrian-German border, and is much too far from either the Swiss or Italian borders for a family to escape by walking. Had the von Trapps hiked over the mountains, they would have ended up in Germany, near Adolf Hitler's mountain retreat.