The real Marta Faria was a talented strong-woman in her own right; she could wrap a steel bar around her arm and once supported the front legs of a large elephant on her shoulders. She was not the slender pianist seen in the movie.
The Nazi stormtroopers in the film are frequently shown armed with rifles and pistols. However, in 1932 the Nazi movement was not yet in power and was considered simply another political party. Armed Nazis on the streets of Germany would have drawn immediate attention and would have been met with force by the police and military.
The actual Zishe Breitbart died on October 12 1925, almost eight years before the events of the film. In the film he dies on January 28, 1933, "only two days before Hitler's ascent to power". This inaccuracy is a deliberate choice and should be regarded as "poetic license" on the part of the director.