While being married to his wife Anna it is shown that Strauss Sr. only had 3 sons, Johann Jr., Eduard and Johann. In real life in the 1840s he had 5 surviving children, including Anna and Therese.
Johann Strauß Sr. died at the age of 45, not 44 as mentioned in the movie.
In a scene after performing his Delirienwalzer Josef Strauss told his wife that he is invited to Petersburg and that he would be the first Strauss to perform in Petersburg. The waltz was composed in 1867. however is brother Johann already performed in Petersburg in the 1850s.
Josef Strauss' "Delirienwalzer" was composed in 1867, a year before Johann Strauss Jr.'s "Unter Donner und Blitz, Polka schnell", while in the movie it was the other way around.
The waltz "Wiener Blut" was composed by Johann Strauss Jr. in 1873, 24 years after the death of Johann Strauss Sr., while in the movie he was still alive during the performance. Same goes for "G'schichten aus dem Wienerwald", which was composed in 1868, while in the movie Strauss Sr. just died, an event that happened in 1849.