Bowdlerize: The French dub removed the renditions of "Maria" and "Climb Ev'ry Mountain" sung by the nuns as they thought it was sinful for nuns to be singing non-religious songs. As such only the reprisals of them were heard. And the subtitles don't show the lyrics to them.
Enforced Method Acting: Christopher Plummer disliked working on the film and isolated himself from the child actors, playing into the stern relationship the Captain has with his children. However, he has mellowed significantly; he and Charmian Carr got on wonderfully well, Julie Andrews counts him among her closest friends and he has come out and said that the first time he sat down to watch the film, he realized it was the greatest cinematic adaptation of a stage musical ever produced.
The scene where the Captain embraces music again and sings with his children was the last to be shot. Since the actors were sad about parting, their tears are real.
I Am Not Spock: Julie Andrews went to great lengths to avoid this. Charmian Carr, on the other hand, has embraced it, writing a memoir of the film/autobiography called Forever Liesl that's a great favorite among film fans. Nicholas Hammond did avoid it, mostly by going to Australia and becoming quite a popular actor there. (He also played Spider-Man.)
One Steve Limit: In real life, one of Captain von Trapp's daughters was also named Maria; in the musical, she becomes a Louisa instead.
Playing Gertrude: Christopher Plummer was 35 at the time of filming (more than two decades younger than his character was in Real Life at the time the story is set), with his oldest daughter played by a 21-year-old actress (playing 16...going on 17).
Nicholas Hammond (Friedrich) had the world's biggest crush on Julie Andrews, as he had seen her three years prior in her last night onstage in London as Eliza Doolittle. This is rather obvious in the film.
Charmian Carr (Liesl) had "a huge crush" on Christopher Plummer, and the feeling was apparently mutual, though things never progressed beyond flirtation. Although she has admitted on the Oprah Winfrey Show's Sound of Music Reunion that he did indeed teach her how to drink.
The Captain was in the Austrian Navy. But wait, isn't Austria landlocked? It was in 1939 but not in 1914, when Austria owned Croatia and had a potent navy dominating the Adriatic Sea. The Captain was one of Austria-Hungary's most illustrious World War I heroes at sea. He commanded two submarines, the U-5 and U-14, and conducted 19 war patrols during which he sank 11 enemy merchantmen, captured a French armored cruiser and an Italian submarine, and was awarded the Knight's Cross of the Military Order of Maria Theresa.
The Maria Theresa order, by the way, is a partial example of this trope. According to legend you get that medal by succeeding in defiance of orders. That is amusing but only partly true. It is for "initiative" not disobedience. It dates back to when the good Empress thought her officers needed a lot of prodding and introduced the medal by her name. It is, however, true that the medal can be awarded for unusually daring and successful initiative, even in defiance of orders that could lead to a court martial if unsuccessful, or even if only slightly successful.
The whistles were real. RL Captain von Trapp had a weak voice. He did not however drill them as if they were in the navy. The family used the whistles to locate each other and communicate across their vast property. The whistles could be heard from one corner to the other, instead of spending hours hunting down a child. They used them as an effective method of communication up until their departure from the country.
In reality, Georg and Maria were married in 1927, and she had borne two other kids by the time they left. Not only that, but they simply got on a train to Italy.
It's a fact of local legend that after the stage musical was written, anytime it was performed within a couple hours' drive of Stowe, Vermont, Maria von Trapp would attend opening night.
The depiction of Georg von Trapp as a stern disciplinarian annoyed his wife, as he was the exact opposite in real life—it was Maria who was the strict one. (She did, however, adore Christopher Plummer.)
In the movie, Georg quickly decides to reject the offer of a Captaincy in the Kriegsmarine and leave Austria as soon as possible. He actually anguished over the decision for a while. Technology had made such big strides since WW 1, plus he had spent two decades as a sea-captain without a sea but was still a U-boat warrior at heart, that the offer to command a modern submarine was very very tempting to him.
Of all the exaggerations of their lives, Maria commented in her memoirs that the only thing they didn't go far enough on was her behavior at the convent. She always laughingly commented when asked if she was that bad, "I was worse!"