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.