In real life, the coronation of Joseph and Elisabeth (Sissi) took place in the Castle of Buda in 1867. However, they couldn't shoot the scene in Buda when this movie was made because the castle was seriously damaged during WWII. Furthermore, there was a revolution in Hungary against the Soviet regime in 1956. This made it impossible to shoot the scene at its original location.
In the movie the Archiduchess Sophie is seen giving back Sissi's baby to her but in real life this was never the case. Sophie found Sissi too immature and young for her to be able to raise properly her children. She then took upon herself to raise Sissi's first three children against her will, this of course brought a lot of conflict between the two women.
Sissi's first daughter died when she was two years old. She got typhoid when they visited Budapest. The film doesn't mention this fact. Furthermore, Sissi and Joseph were crowned only in 1867 as the Queen and King of Hungary.
This movie begins a couple of weeks after Franz Joseph and Sissi got married, which was in 1854. In 1855, Sissi gave birth to their first child. Also, Franz Joseph later references the Crimean War, which lasted from 1853 to 1856. But the coronation in Hungary did not take place until 1867. So about a decade is minimized to a couple of minutes, while a couple of years form the biggest part of the movie.
The war that Franz Joseph mentions to Sissi just before he's about to receive the Hungarians is the Crimean War.