Factual error: As Father Laforgue walks in town at the beginning of the movie (with a better, closer look a minute later before the scene changes), you can see that despite the "Quebec. North America 1634" caption, they have on a pole the contemporary flag of Quebec, designed only in the 20th century. (00:01:55 - 00:02:30)
Character mistake: We see in a flashback (so, early 1600s) the protagonist with his mother in Ruen, back in motherland France. She tells him she is praying to St. Joan (d'Arc; they are in front of a statue of hers). Joan d'Arc wasn't canonized until the 20th century. You could argue that in the eyes of the laymen she was already considered a saint. However, her son does not object and considers her a saint as well, doubling down on the statement even later on in Quebec when he does not have to humour his mother, and he is a Jesuit. He obviously should know better. (00:35:25)