Russian last names are usually declined, especially if they end with "iy" or "ov". They are changed to "aya" and "ova". During the entire movie the male version of the last names are used when addressing or announcing women. So was Katjas last name "Dolgorukova" instead of "Dolgoruki" as said in the movie.
In the movie Katja and Tsar Alexander II first met at the Smolni-institute in 1865. In real life he knew her and her siblings already since she was a 10year old and supported their education since the father died poor. He also proposed his love to her much earlier than in the movie and she agreed only in 1866 until in 1867 their affair became public.
The Tsar attacker from 13th March 1881 was called Nikolai Ryssakow, not Stepan.
The final bomb attack against Tsar Alexander II happened in 1881, which caused his death. It was not done in 1880 during his wedding ceremony with Katja. His final bomb attack which caused his death was caused at 2:25 pm, not at midday. Also the second bomber, Sofia Perovskaya did not die during the bomb attack but was declared to death by verdict a few days later.
The yellow flag with the black double-eagle was used in the Russian Empire until 1858. During the time of Alexander II a tricolor flag with black-yellow-white was used until 1896.
Tsar Alexander II's oldest son Nikolai died in 1865. In the movie he attends his mother's funeral. Tsaress Marie died in 1880.
The movie's plot begins in 1865. The emancipation reform, which was mentioned later in the movie and is canceling the rights for having serfs began and was approved in 1861.
Earlier in the movie set in 1865 It was announced to set up a new Governor for Kazan and General Kernutski was suggested and agreed. At that time Major General Nikhail Naryshkin was Governor and remained it until he was replaced by adviser Nikolaj Skaryatin in October 1866.
It is mentioned that In the 1860 there were 49 millions subjects in Russia. Later in 1880 the Tsar said that he has "100 million students", referring to the population of the Russian Empire. However there were around 80 million people living in Russia at that time.
The revolution attack attempt against the Tsar Alexander II by Alexander Solovyev, who, as said in the movie, became a teacher, was in 1879. He died the same year. However in the movie the event is set after Tsaress Marie's death in 1880.