Factual error: The galley during the battle scene is rowed by slaves. Romans during this time period didn't use slaves to row their galleys. Rowers had to be able fight. If not, the Romans would be outnumbered 200 to 30 when they boarded the pirate ship as the pirates rowers would be able to fight.
Factual error: The actors and stunt drivers use only two reins to control the four horses that pull each chariot in the race. However, charioteers in ancient Rome used separate harnesses with two reins controlling each horse. In a race such as the one depicted in the movie, where four horses draw the chariot (two-horse races were common, as well), a real charioteer from the era would be holding eight reins.
Factual error: Al-Tair and al-Deberan are the names of the Arab Sheikh's horses, and he states they're named after the stars. Those stars were given their names by Arabian astronomers, and calculated astronomy by the Arabs emerged during medieval Islam in the 7th and 8th century CE, 674 years after the plot of the movie takes place.
Factual error: In the movie, Pontius Pilate is appointed to be governor of Judea around AD 32 (Judah is enslaved in AD 28, spends 3 years as a slave and then at least one year with Arrius before he meets Pilate, who is still not appointed). In reality, Pilate was the governor of Judea from AD 26-36.
Factual error: Emperor Tiberius of Rome was a reclusive and vicious tyrant by 26AD when "Ben Hur" is set. Furthermore, by that time, he had retired to Capri and was rarely in Rome. In the movie, he's the picture of Regal benevolence, basking in the love of the crowds and showering glory on Arrias in victory. In real-life that never would have happened. Tiberius' Governor Sejanus would have presided over Arrias' triumph, not Tiberius.