Factual errors: The credits state that the music is all by Prokofiev. However, you can distinctly hear Boccherini at one point. Also, the sonata for violin and piano that Sonja plays with her extra-marital lover is Beethoven's Spring sonata, Op. 24. When Boris is at the opera, it is the Magic Flute, which was written by Wolfgang Amadeus Mozart.
Factual errors: In the scene where Sonja accompanies Beethoven's "Spring" violin sonata, the music on the piano is visibly an orchestral score, whereas the piece they are playing is a duo. Besides, the "violinist" never moves his left hand's fingers.
Continuity: When Boris crawls into the cannon, he is wearing a green French uniform instead of his own blue uniform. (Just before he mentions being behind enemy lines.)