Friends of Goethe continuously refer to him as "Johann", whereas in reality, the name by which he would have been called is "Wolfgang". In 18th century, the first name usually was usually handed down from the father or some other important relative (Goethe's fathers name was Johann Caspar Goethe), whereas the second name was the one through which a person gained its individuality. Therefore, it was the one used by friends and family.
As in the movie Goethe didn't pass his doctoral exam in Straßburg. But in real life because of drafting the 56 theses of the 'Positiones juris' it was enough for Goethe to gain the degree of the licentiate of Laws. This allowed him to open an own law office.
The copy of "The Sorrows of Young Werther" is clearly a paperback edition with a glued binding in a soft cover. In 1774, such mass produced bindings were unknown. The printed pages would have been in joined together in a sewn binding, which would then be connected to the front boards of the book.
Goethe is singing Lotte and her siblings the Canon 'Bona nox! (KV 561)' by Wolfgang Amadeus Mozart. It was written in 1788, 16 years after the plot's setting.
The duel between Johann Goethe and Albert Kestner didn't exist in real life. However it is known that Goethe was wishing Kestner his death. The movie's producer Christoph Müller said, that it was known but they wanted to do it more cinematographic and not as a dialog line.