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.
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.
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.