The young Boris has blue eyes, but the adult Boris has brown eyes.
When Boris goes to see Sonia before his duel, he suddenly kneels down ("To die before the harvest..."), then a split-second later he's back up again.
Early in the movie, Boris notes that Old Gregor is younger than Young Gregor. In Boris' reflection near the end of the movie, he refers to them as Old Nehamkin and Young Nehamkin.
During the boot camp "training montage" Boris's uniform changes between one with black cuffs and collar and one with red cuffs and collar.
48 minutes in, Sonia fills the same cup with tea twice.
The credits imply that the music is all by Prokofiev. However,
you can 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 Mozart.
Boris's Father's small piece of land would be subject to the laws of communal ownership in the era depicted.
Boris calls Anton "Quasimodo", a reference to the title character in the Victor Hugo novel "The Hunchback of Notre Dame". The film takes place during the Napoleonic Wars, which ended in 1815. "The Hunchback of Notre Dame" was published in 1831. But the movie doesn't pay much attention to historical accuracy to begin with, so it's fair to say the insult was meant to be part of the spoof.
Klieg lights can be seen reflected on Boris's eyeglasses and in the eyes of several characters in numerous scenes.
In the duel scene the behavior of the snow when walked on reveals it to be foam.
When Sonja (Diane Keaton) 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.
During boot camp, the line of soldiers draw their swords and charge down the field. When they charge back towards Boris and the camera, one of the solder trips and falls down.
In the battle scenes the infantry use percussion cap muskets, which were not invented until after the Napoleonic Wars.
Sonja has had modern dental work done.
In the closeup of Boris' face during Napoleonic battle scene, the reflection of a man holding a boom mic is visible on Boris' glasses.
When Boris asks Sonya to "guess who" when he places his hands over her eyes, she says that she would recognize those hands anywhere and says "Old Nehampkin". As Boris's cousin and someone who was familiar with old Nehampkin's hands, she should have realized that Old Nehampkin had died 25-30 years earlier in a lightning strike.