There is no evidence that Emperor Franz Joseph sexually assaulted Sisi. They had genuine friendship with each other towards the end of her life.
There is no evidence that Countess Irma Sztáray had romantic feelings for Sisi. They were just close friends.
Sisi did not have Countess Sztáray murder her and place the blame on anarchist Luigi Lucheni. Lucheni had planned to assassinate Prince Philippe, the Duke of Orléans, but the Duke could not be found. Lucheni chose Sisi after reading in a Swiss newspaper that she had traveled to Geneva.
The real Queen Victoria was wearing black after the death of her husband Prince Albert, which she doesn't do in the movie, set in the 1880s-1890s.
Irma Sztaray started her duty as Sisi's handmaiden at the age of 30, while in the movie she says that she is 42.
In the Church scene the Ulrainian folk song "Shchedryk" (also known as "Carol of the Bells") can be heard in the famous version adapted by Mykola Dmytrovych Leontovych. While the folk song already existed in the 19th century, it was unknown outside of the Ukrainian regions and was only known in Europe as of 1919, 21 years after Sisi's death.