Conrad, Marquis of Montferrat, is described as a "wise Venetian" in the script, ignoring the fact that his title indicated where he is from. Montferrat (Monferrato) is in Piedmont, in NW Italy; Venice is in the NE.
Much of the heraldry depicted is incorrect. The arms of Montferrat are argent, a chief gules (white or silver, with a red band at the top), not the fanciful design with fleurs-de-lys depicted in the film.
Saladin is depicted as ignorant of the existence of ice. In fact, ice was found in the mountains of the Middle East, and was used to cool drinks. Saladin famously offered King Guy of Jerusalem a cup of iced water after the battle of Hattin, in an incident which led to the killing of Reynaud de Châtillon, Lord of Oultrejourdain.
During the joust scene, in the first pass the combattants correctly gallop with the central barrier on their left (shielded) side. In the second pass, they wrongly gallop with the barrier on their unshielded side.