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.
Continuity mistake: During the boat scene, the baroness leaves and walks behind Maria. From the immediate opposite shot the baroness has vanished.
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.
Audio problem: When Georg playfully taps Max's cheek, we hear 3 taps but Georg only taps twice.
Continuity mistake: When the captain sings for the first time and hugs the children, Gretl is under his left arm. In the next shot, he raises his arm and she is nowhere to be seen. Then, when Maria motions for Gretl to give the Baroness the edelweiss, she is back under his arm.
Answer: Postulants/Novices, such as Maria, were forbidden from singing in the Abbey. However, these rules did not necessarily apply to the sisters who are singing. In addition, it's a musical, and the nuns weren't "really" singing. Their complaints about Maria are simply put into a song.