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: 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.
Trivia: Although the movie was almost a completely different story than the book, they did make reference to a scene in the book: when you see the guy in the beginning in the hospital, he has blood all over his face. The reason is because right before then he was talking about Quantum Foam and then went into convulsions, then started spewing up blood...gory, but a nice add in to let us know that the writers actually read the book.