When Stalin receives the order about burning down places around Moscow he seems surprised and asked what would happen with the people. However in real life this order (Order Nr. 428) was done by him himself and Marshall Boris Shapishnikov and was finally released on the 17th November 1941. So this shouldn't have been a surprise for him.
According to those who knew Zoya and the memories of Zoya's mother, Zoya was very calm, confident and not very girly, which is quiet different than how she is portrayed in the movie. Furthermore she didn't have a boyfriend as shown in the movie.
Semen Sveridov was shown trying to save Zoya twice from the Nazis. In real life he reported about her to the Wehrmacht officers right away.
It is known that when arriving in the Moscow region Wehrmacht soldiers felt cold, especially since they didn't have any winter clothes and later they didn't arrive since they were blocked on the way. Therefore they stole the clothes from the soviet citizens. In the movie the Nazi soldiers received their clothes and didn't steal anything.
The first scenes of the movie, set in October 1941 in Moscow the city is shown as calm and clean. It is unlikely to be like that since the Nazi attacks on Moscow already began on the 2nd October 1941.
When Zoya is walking through the snow after her arrest during the night there is no steam coming out of her mouth, which should happen during winter.
When Zoya is checked to become an agent, the officer is talking German to her. His subtitled line "In your questionnaire it is said that you learned German in school" is translated very incorrectly into the real German, including "es ist gesagt" (for "It is said") "Das Sie studieren Deutsch"". The real line should have been "In deinem Fragebogen steht, dass du in der Schule deutsch gelernt hast". Furthermore the word "Du" (Singular "You") was translated as "Sie" (plural version of "You").