Oh, Jane is perfectly okay.
Historical inaccuracies are unavoidable - and after all, films such as this are intended and marketed as fictions, not documentaries (and even those are just interpretations of whatever source material is available). I do not mind when verisimilitude is sacrificed for the sake of narrative coherence and dramatic tension: in fact, I'm even expecting it.
For example, it did not bother me at all that they included the "here I stand, I cannot help it, God help me"-speech, even if it is most likely an apocryphal legend that first appeared almost a century later in writing: it's a good speech, and it's what you'd expect at such a pivotal point in the narrative.
However, Luther was a brash, "loud" character with a mind of his own - not a saintly, soft-faced Joseph Fiennes who took care of crippled children while contemplating religious liberty. In fact, it was the final note of the film that annoyed me the most, with the reformer joyously declaring that the emancipation of Protestantism constitutes a victory for freedom of religion.
Neither Luther nor the other Protestant reformers were interested in granting all religions the same status, and letting each individual choose their own path as a private decision. Luther turned bitterly upon the Jews (whose printing presses had aided considerably in the spread of protestantism) when they proved resistant to proselytizing; John Calvin had the Unitarian Michael Servetus burned at the stake to prevent his doctrinal "poison" from spreading, etc.
I didn't expect the film's authors to include Luther's antisemitic writings (which read like a road map for the Holocaust) in their script, but they specifically went out of their way to assert an idealized image of the man.
