Corrected entry: When Luther is talking to Katie after she sings to him, he says "people try to make me out to be a fixed star, but I'm not. I am a wandering planet." The planetary model in which stars are fixed (relatively speaking) and the planets are in motion was put forth by Galileo, who was not born until 1564. The scene in the movie takes place shortly before 1530, when the geocentric model of the universe was still the prevailing thought, even among an educated professor, such as Martin Luther.
Corrected entry: In the scene where the Monk selling scrolls is trying to convince a crowd to buy, he puts a torch under his hand and you can visibly see his hand burning. In a shot closely after that his "burnt" hand is outstretched, and unburnt.