Revealing mistake: At the end of the movie, where Commisar Niemans and his partner are in a firefight with a group of "angels", one of the bad guys is firing a Minimi machine-gun. When the camera zooms in, you can see that the weapon is fed with blank rounds.
Factual error: Marie discovers that letters in a 9th century ornament are actually Arabic numerals. Those were not introduced into Europe until the 13th century and although the numbering system was already in use in Arabia, it used different glyphs than the ones she identified.