In the film, the Nazi troopers who persecute the Von Trapps are all in brown shirts and were a group known as the SA. In reality, Hitler eliminated most of the SA in 1934 during the Night of the Long Knives and began using the SA, who wore balck shirts. The Sound of Music is set in 1938
Should that really be considered as a 'slip-up'? I mean, a lot of movies based on historical events or based even on people don't get the facts 100% correct. It's not that big of a deal. Besides, that's Hollywood for you.
Although the SA underwent 'purging' during the Night of the Long Knives, only the high officials of the SA were eliminated. The SA (the 'Stormtroopers' or the Brownshirts)were kept but only as subordinates to the SS or the Blackshirts.