Plot hole: Throughout the film, anybody who speaks English uses Modern English, with either a British or French accent as appropriate. However, 1357 was solidly in the Middle English period. Although that language would not be utterly incomprehensible to modern-day travellers, neither would it be indistinguishable as it was in the film. The film specifically draws the viewer's attention to language at several points, making suspension of disbelief impossible. The French speak French, and very few of them speak English. There is a scene in which Andre is talking to Claire, and her lack of knowledge of modern idioms makes the conversation difficult; that should be true for all characters at all times. If the historical people were talking alone among themselves, I could accept that they're being "translated" for us. But they're talking directly to the modern travellers - it's too jarring.
Plot hole: At the very beginning of the film, the historical record reflects what appears to be the original series of events. However, all of the physical evidence reflects the various changes made by the characters throughout the movie. The most glaring example is the fact that history records the hanging of Lady Claire, which motivated the French peasants to the point that they successfully took the English held castle. However, they also find the sarcophagus, which contains the remains of Lady Claire and Andre Marek, from when they died some twenty five years after the battle, because he went back in time and saved her life. But if Lady Claire is in the sarcophagus, then she wasn't hanged in 1357 and it wouldn't be a matter of historical fact. Both set of circumstances can't be true at the same time.