During the first half of the scourge scene, Jesus' hands are dark and bloodied by his shackles. Then a dramatic close-up shows them nearly clean.
In the flashback scene where Jesus kneels to draw a line in the sand, he reaches across with his right hand. The hand that actually draws the line is a left hand, with the palm facing away.
The lead Roman soldier's teeth are yellow during the flogging scenes, white and perfect along the route to Golgotha as Jesus is carries the cross, and yellow again during the crucifixion scene.
As Jesus carries his cross, the blood on the cross disappears and reappears between shots.
A shawl appears on Mary Magdalene's head between shots after Jesus, on the cross, says, "Son behold your mother...".
Latin and Aramaic are spoken throughout, but Greek is not spoken or used at all. Greek was the common language of the eastern Roman Empire. The accusation on the Cross of "Jesus of Nazareth, King of the Jews" was written in Greek as well as Aramaic and Latin; the sign is shown, but no Greek.
When Mary cleans the tiles of her son's blood splatters, the blood is still liquid. It would have coagulated, then dried in the heat.
Differences with the written source material are not counted as goofs, especially when they're caused by dramatic decisions. Historical inaccuracies are similarly exempt, especially when caused by reliance on religious and artistic traditions.
Silk road traders from Mongolia and China used domestic Bactrian (two-humped) camels. It's unlikely, but not impossible, that they would turn up in the Middle East, the Silk Road's western terminus.
Just after Jesus' appearance in front of Herod, Pontius Pilate claims he had put down rebellions in Judea for eleven years. Pilate was prefect (not procurator) of Judea from 26 CE to 36 or 37 CE, and had been so for only seven years when he met Jesus. But not much about Pilate is known, and he could have been in Judea in another position before that time.
Satan moves through the crowd while Jesus is being beaten. Jesus is the only one who is supposed to be able to see Satan. However, one man in the crowd follows Satan with his eyes as Satan moves past him.
Jesus' computer-generated brown eyes sometimes fade into Jim Caviezel's blue ones. This happens when Jesus is taken at Gethsemane, and again after Jesus has first taken the cross on his shoulders (before the shot with the donkeys and palm leaves in the background).
Flipped shot: Jesus stumbles and falls to the ground while carrying the cross, his injuries are to his left eye for one shot. By the next shot the injuries have returned to his right eye.
Before Judas commits suicide he puts his hands to his face. The makeup on his right hand is peeling away.
Jesus' arm is dislocated to make his hand reach the nail hole, so his arms should be fully extended and straight at all times. However, in almost all shots of him on the cross, his body sags forward with his arms bent at an almost 90 degree angle.
Throughout the movie, characters speak Syrian Aramaic, which was used in the 7th and 8th centuries CE, not the 1st century CE Palestinian Aramaic they would have used.
At about 16:30, as the guards are calling "priests" to the temple a guard and priest are in doorway, as the guard turns around he is very clearly wearing aviator style sun glasses. Visible for several seconds.
When Mary goes to clean the blood, as the camera pans over the bloody cobbles, the boom is reflected in the largest pool of blood.
When Jesus is being whipped, one soldier counts the lashes in Latin. He pronounces 18 and 19 correctly, but mispronounces 28 and 29. He is supposed to say 'duodetriginta' (28) and 'undetriginta' (29) but he says 'vigintiocto'.
While Pontius and his soldiers speak Latin, you can hear wrong pronunciations. They tend to say 'fachere', 'dichere', 'fachit' while they are supposed to say 'fatsere', 'ditsere', 'fatsit' or 'fakere', 'dikere', 'fakit'.