Konrad Koch never taught English. He also didn't start as a new teacher in Braunschweig in 1874. He started as a teacher in 1869 and was teaching German and old languages. He also played outdoor games in 1872, two years before the plot setting.
Konrad Koch never studied in Oxford, as suggested in the movie. He studied theology and philology in Göttingen, Berlin and Leipzig.
The movie portrays Konrad Koch as a single fighter who introduced football to Germany. However he did it with his colleague August Hermann who also started in 1869 at the Martino-Katharineum in Braunschweig. He however is not portrayed or mentioned in the movie at all. He and Koch both worked together to introduce outdoor games in the school, including football and later cricket and a basketball-like game.
Medicine balls were just invented in the United States about the time this film is set (1870s) and not introduced to Germany until the early 20th century.
Schricker's price sign tells the price for the balls in "Reichsmark". However, the currency in the German Empire was only called "Mark" (later commonly referred to als "gold mark"). It did not become "Reichsmark" until fifty years later, in 1924.
Newspapers were not able to print photographs in 1874. The first printed photographs appeared in the United States in 1880 and, with Georg Meisenbach's autotypy technique, in Germany in 1883.