In the opera-house sequence, the characters watch the soprano sing the mad scene from the opera "Lucia di Lammermoor" and then one of them says he's leaving before the second act begins. The "Lucia" mad scene occurs during the opera's third and final act.
Leopold tells Victoria that if his wife Charlotte (The daughter of Victoria's uncle George IV) and their newborn son had not died Victoria would have lived a small life in Coburg. However if Charlotte and their son had survived Victoria probably would have never been born. It was the death of the two heirs of the throne that forced the younger sons of George III to marry so that they could produce the next heir. The oldest of the children that survived was Victoria.
Tsarevitch Alexander (later Alexander II) of Russia tells Victoria that his father has chosen a Danish princess for him to marry. While it is possible that the woman he is referring to is fictional, it is more likely an error. Alexander II became engaged to Princess Maria of Hesse and by Rhine in 1840 and married her in 1841. His son, Alexander III, married the Danish princess Dagmar in 1866.
In many of the ballroom scenes they are playing waltzes by Johann Strauss II, which were not composed until many years later. For example, in early 1840, when they are discussing possible marriage suitors, she dances with Sir John Conroy to the waltz 'Wein, Weib und Gesang' (Wine, Women and Song) which was first performed in 1869.
Victoria's mother asks her brother Leopold for money and he tells her that Belgium is a tiny country and doesn't have much. In real life as the widower of Charlotte Princess of Wales (the daughter of King George IV) he was awarded a significant amount of money from England. He also did help his sister and niece with money over the years.
Grand Duke Alexander says he is to marry a "Danish Princess". This Grand Duke Alexander is the future Alexander II who married a German Princess from Hesse-Darmstadt. It was the future Alexander III (who was not born at the time shown) who married a Danish Princess.