Contradiction with Luke 23:1
This verse describes Jesus being brought to Pilate by the whole multitude, while Mark 15:1 focuses on the chief priests, elders, scribes, and the council.
Luke 23:1: And the whole multitude of them arose, and led him unto Pilate.
Contradiction with John 18:28
This verse states that Jesus was led from Caiaphas to the hall of judgment early, while Mark 15:1 gives no indication of that location.
John 18:28: Then led they Jesus from Caiaphas unto the hall of judgment: and it was early; and they themselves went not into the judgment hall, lest they should be defiled; but that they might eat the passover. [the hall...: or, Pilate's house]
Contradiction with Matthew 27:2
This verse implies Jesus being bound when delivered to Pilate, but Mark 15:1 does not mention binding.
Matthew 27:2: And when they had bound him, they led [him] away, and delivered him to Pontius Pilate the governor.
Contradiction with John 19:14
This verse states it was the preparation of the Passover and about the sixth hour when Pilate presented Jesus, whereas Mark 15:1 describes events early in the morning.
John 19:14: And it was the preparation of the passover, and about the sixth hour: and he saith unto the Jews, Behold your King!
Contradiction with Acts 3:13
This verse speaks of Jesus being delivered up and denied in the presence of Pilate, which subtly differs from the account in Mark 15:1 of the council's actions without mention of denial.
Acts 3:13: The God of Abraham, and of Isaac, and of Jacob, the God of our fathers, hath glorified his Son Jesus; whom ye delivered up, and denied him in the presence of Pilate, when he was determined to let [him] go.