The movie opens in "1875 Imperial Russia". A few minutes later, a self-propelled model train is seen in action. Clockwork model trains were first introduced by the pioneering German toy company Marklin in 1891.
The label of the bottle of morphine Anna drinks from changes from "la Morphine" to "Morphine" between shots. The only correct French form would be without an article (prescriptions would have been written in Latin in 19th-century Russia anyway).
(at around 32 mins) While Anna is traveling on a train she was reading a book which was supposed to be in Russian. However, the word that appeared on the screen was in Hungarian "olajfestmény" meaning oil painting.