In the movie Luther quotes the Bible by chapter, and verse. Versification of the Scriptures was not added until five years after Luther's death in 1546. The French scholar-printer Estienne introduced verse numbering and divisions in his Greek-Latin New Testament in 1551. In 1552 he printed a French-Latin New Testament, also with the verse divisions. And in 1553 he printed a French translation of the Bible with verse divisions throughout. Within the same decade the system of verse divisions spread widely, influenced by the adoption of this system in the Geneva Bibles.
When Frederick the Wise is directing Spalatin on how to respond to the summons for Luther from the Cardinal, he talks about letting the "inertia" of the situation take its course. Presumably this conversation takes place on, or around, 1518 (and certainly before the Diet of Worms in 1521), however, the term "inertia" was first used by Johannes Kepler in works published from 1618 to 1621 nearly 100 years later.
When the sacbuts (an early form of a trombone) are playing, one of the sacbuts has a spit valve (or water key) on the end of the slide. Spit valves were not invented until after the 1870's. Also, that sacbut is gold lacquered, which was not done to these instruments at that time.
When Luther is preaching to the congregation, he is walking around, whereas preachers of the time would have stayed in the pulpit. And the congregation is seated by families in pews. Pews were rare in those days--most people stood, and were generally segregated--men in one area, women and children in another.
During the Indulgence scene with Johann Tetzel, the camera cuts to a close up of the hand above the torch, where one can see the heat resistant gel on the (presumably the stunt double's) hand in the flame. It is most visible on the thumb.