Armand Hammer's first visit to Soviet Union was in 1921, not in 1919 as suggested in the movie. Also since he was a medical student it is very unlikely that he did business with Leo Trotsky.
When Ostap and Ibrahim being arrested one of the officers quoted Lenin's famous line "Of all kinds of art the most important one for us is cinema". This line was said by him in 1922 during a talk with revolutionary Anatoli Lunacharski and published in 1925. The movie scene however is set in 1919.
Mishka Yaponchik's father Mendel Vinitski appears in the movie set in 1919. In real life he died in 1897.