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.
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.
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.]