Contradiction with Matthew 27:24
Pilate washes his hands to show he is innocent of Jesus' blood, whereas John 19:13 presents him as actively making the judgment to crucify Jesus.
Matthew 27:24: When Pilate saw that he could prevail nothing, but [that] rather a tumult was made, he took water, and washed [his] hands before the multitude, saying, I am innocent of the blood of this just person: see ye [to it].
Contradiction with Mark 15:15
It depicts Pilate as wanting to satisfy the crowd rather than making a firm judgment from the judgment seat like in John 19:13.
Mark 15:15: And [so] Pilate, willing to content the people, released Barabbas unto them, and delivered Jesus, when he had scourged [him], to be crucified.
Contradiction with Luke 23:4
Pilate declares Jesus innocent, contradicting his action of bringing Jesus out for judgment in John 19:13.
Luke 23:4: Then said Pilate to the chief priests and [to] the people, I find no fault in this man.
Contradiction with John 18:38
Pilate finds no fault in Jesus, which contradicts the act of bringing Jesus forth for judgment in John 19:13.
John 18:38: Pilate saith unto him, What is truth? And when he had said this, he went out again unto the Jews, and saith unto them, I find in him no fault [at all].