Movie: Caiaphas and other priests ("the Jews" in the Gospels) are in charge, convicting Jesus of blasphemy in a trial the Romans do not appear to know about
Facts: Caiaphas was Pilate's subordinate, only Rome could execute, and the Gospels' trial scenes do not justify the 'blasphemy' charge against Jesus

Having seen the movie, Gibson's portrayal of Matthew 26:57-67 seems to be fairly accurate, even down to the words that were spoken. This session takes place before Jesus was handed over to Pontius Pilate. Obviously the Jews had no power to execute, but this council strengthened their resolve in convincing the Roman government to do their bidding.

Also note Matthew 27:1, which is further evidence that the Jewish chief priests' plans to have Jesus put to death. Despite Jesus' prominence, they might have easily had him killed in secret by their own devices, similar to the martyrdom of Stephen in Acts.

The movie also seems to correctly portray the apprehension of Pilate to have Jesus unjustly crucified as stated in the Gospels.