The name of the warlord, Bayan, is alternately pronounced "By-an" (the correct pronunciation) and "Bay-an" by different actors throughout the film.
Tris, a mere bowman, would not have been able to read or write,
In the escape, the first of the arrows fired by Tris has a flat, possibly rubber, 'point'.
During their escape from the Chinese palace, Tris shoots an arrow into the forehead of what is an obvious dummy.
When the tribesmen ride away from the burning city, in the wide shot, the action wobbles the matte painting of the background, roughly just below the top of the trees.
It's interesting, and pretty hilarious, that the longbows release their arrows with the sound of a pistol shot.
It's the 13th Century when our heroes first leave England. Walking through the Arab market, they pass tomatoes for sale, which are later thrown at them by children. Tomatoes are a New World plant, and could not have been found in Old World markets prior to the voyages of Columbus in the 15th century.
Walter uses the term "men of science" is near the end of the film. The term "science" did not appear before the 1830's.
In the movie Maryam was excited to receive black hosiery. Hosiery however was not introduced in England till the 16th century and at that time Warren only by men.