The movie shows Magnus Hirschfeld's practice in 1895 in Berlin. However in 1895 his first medical practice was in Northern Magdeburg and didn't move to Berlin-Charlottenburg until 1896.
The event in which Hermann von Teschenberg was caught kissing a soldier in the Vienna Prater was in the late 1880s when Teschenberg was in the early 20s. In the movie the event is set in 1894.
The composite sketch of Hirschfeld in 1897 resembles more Hirschfeld in his older years in the 1910s rather than how he (or rather the actor Kai Schumann) looked like.
In a scene in 1896 Magnus Hirschfeld is holding an edition of Adolf Brand's magazine "Der Eigene" with a cover that was first used in July 1899.
The Prussian Officer is holding a newspaper "BZ am Mittag" that first was printed in 1904, 9 years after the scene's setting.
The term "Transvetite" was introduced by Magnus Hirschfeld in 1910, not in 1896, as shown in the movie.