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).
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'.
When Jesus encounters the woman caught in adultery, she has wounds from being struck with stones. However, she was never stoned in the Bible. Jesus confronts her accusers and says, "Let he who is without sin cast the first stone", and her accusers walk away.
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, 10 or 11 years. If Jesus was put to death in 33 CE, Pilate had been in Judea for seven years.
Differences with the written source material, especially relating to artistic decisions, are not counted as goofs. Historical inaccuracies are similarly exempt, especially when caused by reliance on sectarian traditions or Renaissance/Baroque art.
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' 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.
No matter what Judas does, he cannot hurt or stop Satan's demon children, who begin to harass him. Yet, as they chase Judas along a sandy stretch on a small hill, he scoops up a fistful of dirt and throws it back at the children. The dirt hits a child actor on the head, and he nearly stops dead.