Factual error: Professor Harold Hill asks the mothers of River City about their sons, "Is he starting to memorize jokes from 'Captain Billy's Whiz Bang?'" While the film is set in 1912, the first issue of the pulp magazine, "Captain Billy's Whiz Bang," did not appear until 1919. "Whiz Bang" was a term coined by soldiers in World War I (commencing in 1914), which referred to a rocket that "whizzed" by and exploded with a "bang."
Factual error: At the start of the movie, the train the salesmen are on travels from Brighton, Illinois to River City, Iowa. The entire time we see, through the car windows, lush, green farmland. The problem is, to get from Illinois to Iowa, one must cross the Mississippi River, which is over a mile wide, but there is never any sign of either a river or a railroad bridge.