At the Vienna Congress held in 1815 the orchestra in a canteen played Franz Schubert's "Military March," which was composed in 1818.
The Russian anthem "God Save The Tsar!" accompanying Alexander's official arrivals in the movie has in fact been adopted in 1833 (i.e. 18 years after the depicted events).
The Gala Opera performance features Borodin's Polotsvian Dances. These were first performed in 1890, sixty-five years after the film is set.