Factual error: In the very beginning, the doctors are working to revive the man found in the desert. You can see the heart monitor is flatlined and they get out the paddles to shock his heart back into rhythm. However, even when he is shocked by the paddles the monitor doesn't register anything. The shock from the paddles alone would have made the heart monitor spike up for that second but you can see it's flatlined the entire time.
Revealing mistake: When Kate, Chris and Lord Arnaud are in the hidden monastery tunnel, there is an explosion that shows them the way out. One of them crawls forward a little and puts his weight down on a big chunk of stone, which flips about like it weighs nothing. It's very obvious that it's a piece of styrofoam rock. A piece of stone that size would not move as freely as this one did from just leaning on it.
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.
Revealing mistake: When Chris brings the beers to Kate's excavation area and startles her, she then sits up and proceeds to turn down her iPod. However, she turns the wheel on the iPod clockwise, and for those of us who own iPods, we all know that either that scene was reversed, or she blew her eardrums out so she would not have to listen to Chris.
Factual error: Both the English and French armies are wearing uniforms (English red and the French blue). An army would not have had a uniform at this time - each knight would have his own standard and colours - these colours would also have been worn by his squires. The peasants (bowmen) would wear their own clothes - usually a brown or other earth tone, and definitely not a red/blue tabard.
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.
Continuity mistake: Near the beginning of the film, Kate finds a bas relief that has been partially destroyed and replaced with unadorned stone. As it turns out, she destroyed it herself in the past. However, when she does so, she eradicates almost the entire framed portion. In the present day, only the lower part had been dismantled.
Factual error: Though an understandable mistake, it is worth noting that the medieval people are all speaking modern English. Before they leave, the group insists upon the French guy coming to translate for them, but they would hardly have been able to communicate with the English speaking people of the 1300's themselves. Lord Oliver and the English would have been speaking Middle English like in Chaucer's "Canterbury Tale's", and I doubt they would have been able to understand them any better than the French (who would not have been speaking modern French either). [This is covered in the book, as some people have noted, but doesn't apply here. In the book they're given translation devices (if I remember rightly), which let them understand but not talk back. Fine for the book, as throughout that the communication barrier is made clear, but here it's not relevant, as they understand everyone perfectly. "Movie language", ie. where everyone foreign speaks in English but with an accent doesn't apply either, as that's normally reserved for communication within the same group, not between cultures.]
Continuity mistake: In the scene just before the group is sent back to 1357, as they are standing in position inside the time machine, Doniger calls up to Stern, who is waiting at the top of the stairs, "Josh, come down!" However, exactly before this, Josh Stern can already be seen descending the stairs to join the others, although when Doniger calls up to him, he appears at the top of the stairs again.