Factual error: Aside from the fact that split-level entries didn't exist in 17th century Austrian palaces, there would be no windows in main state rooms if you did enter the front door and step down.
Factual error: The von Trapps are shown walking over the border to Switzerland after a short drive out of the centre of town...except Salzburg is about 200km east of Switzerland. If one walked across the border at Salzburg, you'd be entering Germany, which is where (I believe) the people they were trying to get away from lived. Take a look at a map.
Suggested correction: Even though the von Trapps were 200km from the Swiss border, in the last 5 mins, they received a car from the sisters at the convent and the sisters disabled the cars of their pursuers.
Captain Von Trapp was clear, when they were about to hide, that they would drive into the mountains in Salzburg (which the movie did a close up on to show it was those mountains specifically) and walk over them on foot confirming the movie is pretending those are mountains into Switzerland. The director himself admitted this when the real Maria Von Trapp complained of this error. He said "In Hollywood you can make up your own geography."
Factual error: At his wedding, Captain Von Trapp is wearing three medium-width rank rings on the cuffs of his uniform (similar to a Commander in the Royal Navy and US Navy). In the Austro-Hungarian Navy, in which he served, this rank badge did not exist. Von Trapp actually held the rank of Korvettenkapitän (Lieutenant-Commander), indicated by one medium ring and one narrow ring. Even had he held the rank of Linienschiffskapitän (Captain), he would have worn one medium and three narrow rings. The only rank which had vaguely similar insignia to that in the film was Linienschiffsleutnant (Lieutenant), with three narrow rings. Even allowing for artistic licence re Von Trapp's actual rank, the insignia he is wearing simply did not exist.
Factual error: The von Trapp family's eating habits do not match the time and place. eg. They cut up all of the meat on the plate into bitesize pieces, then put down the knife, take the fork in the right hand and continue eating with only the fork. This would not have happened in an Austrian family of their rank at that time in history.
Factual error: When the Von Trapp family is hiding in the Abbey to avoid the Nazis, they are hiding behind some headstones. In reality, these headstones are flush against the wall and no one would be able to fit behind them.
Factual error: When singing "Do-Re-Mi", Maria is playing a Goya guitar. Goya brand guitars were not invented until the mid-1950s, a good ten years after this takes place.
Factual error: The story is set prior to the Anschluss, which was Austria's forced annexation with Germany in 1938. At this time Austrian vehicles still drove on the left (Hitler eventually changed that). When Von Trapp brings the Baroness to his home for the first time, he drives on the right.
Factual error: When they're making their escape in the Citrôen a shot is shown under the car. The tyres on the Citrôen are "Michelin X" radials. These were not on the market till 1948.
