The Shah offers Jamuga both his daughters. Muslim men are allowed to have multiple wives, but not close relatives, and they can marry one at a time. A Muslim woman cannot marry a pagan.
Genghis Khan didn't start the war at Khwarezm. The Shah killed the messengers of Khan, who started a bloodbath in revenge.
In a film about Mongols and Chinese, no Asians in the cast have speaking roles. Several actors have blond hair and blue eyes. In real life, some Mongol and Turkic tribes have fair hair and/or blue eyes Genghis Khan was likely a red-haired Scythian.
The hole in Temujin's wooden collar is large enough for him to slip through easily while still locked. The collar Jamuga wears later is appropriately tight and secure.
In the beginning, when Jamuga hits young Genghis Khan and throws him on the ground by the river, the round yoke around his neck bends twice, as if made of foam or another material, instead of wood.
Chinese men wear their hair in a pigtails. At the time, men wore long hair in a topknot. They didn't wear pigtails until the Qing/Manchu dynasty (1644-1912).
James Mason uses a glass mirror to signal the emperor's soldiers. Glass mirrors were invented in 1835. In the time of Genghis Khan, polished metal disks were used as mirrors.
In the fight between Bortai and Jamuga, Bortai's slip appears twice.