(at around 40 mins) When Judah holds the small sword at the throat of the Roman after his arrest, it is right up against his skin. In the flashback later in the movie (at around 1h 27 mins), the sword is much lower and not directly against his throat.
(at around 33 mins) As the Romans march into Jerusalem and the officers talk security, the distance between Pontius Pilate, Messala and their mounted officers varies between shots by quite a few horse lengths.
(at around 33 mins) As the Romans march into Jerusalem, establishing shots show the Roman soldiers lining up across the entire visible length of the city's main street, and Pontius Pilate rides in the very center. As soon as the column reaches the house of Judah Ben-Hur though, we suddenly see the very end of the column as if Pilate had inexplicably fallen back in line or the column had shrunk.
(at around 1h 13 mins) After Judah punches & knocks Messala into a large puddle of water, Messala lands on his back and is half-submerged in water. When he stands up, however, the back of his head looks completely dry.
The Sheik played by Morgan Freeman has Bactrian (2 humps) Camels in his camp and caravan. Bactrian camels are found in the Central Asian Steppes not in the Middle East. Dromedary (single hump) camels are the ones you would find in Arabia and Middle East.
(at around 1h 40 mins) Ben-Hur is dragged along by his chariot for at least a minute of screen time but suffers no damage to his clothing or his body.
(at around 1h 45 mins) According with Holy Gospels, Christ was arrested by Temple soldiers, not by Romans. At this time Judea was a reign under roman control but with his own laws and "police". Only Romans can execute to death, so Jesus was bring to Pontius Pilate after a Jewish trial.
The opening sets the date as "33 A.D.", but the grammatically correct way to date years after the birth of Jesus is A.D. 33 ("Anno Domini 33"). Only B.C., or the more contemporary BCE, are listed after the year.
Every roman soldier has red clothes. Red clothing was extremely expensive at the time, and only high ranking roman military officers, such as centurions had clothing of such color.
(at around 54 mins) As Judah struggles to remove the chain from his shackles under water, he pulls the chain over his shoulder where the links hover momentarily where iron links would sink instantly from their weight and sink down from the shackle and his hands. A material only moderately heavier than water would hover as shown.
The women Naomi, Tirzah and Esther all have shaved armpits, quite inaccurate for 1st century Jews.
(at around 12 mins) As Judah walks through the market, the traders are emptying baskets of chili peppers that fill the entire foreground of the shot. These peppers were introduced to the world when Diego Álvarez Chanca, a physician on Columbus' second voyage to the West Indies in 1493, brought the first chili peppers to Spain and first wrote about their medicinal effects in 1494.
(at around 19 mins) When Esther is with Ben-Hur at the marketplace, she is wearing modern pants.
(at around 1 min) In the opening scene Judah and Messala are racing horses with saddles having stirrups which weren't introduced into Europe for another 700 or 800 years.
Some of the clothes have been obviously manufactured with modern techniques.