Contradiction with John 14:9
Jesus' statement "he that hath seen me hath seen the Father" can contradict Luke 9:20 if interpreted as an indication of divinity that Peter's confession does not explicitly affirm.
John 14:9: Jesus saith unto him, Have I been so long time with you, and yet hast thou not known me, Philip? he that hath seen me hath seen the Father; and how sayest thou [then], Shew us the Father?
Contradiction with Mark 3:21
Here, Jesus’ own family thought he was "beside himself," which contradicts Peter's recognition of Jesus as the Christ in Luke 9:20.
Mark 3:21: And when his friends heard [of it], they went out to lay hold on him: for they said, He is beside himself. [friends: or, kinsmen]
Contradiction with Matthew 16:16
Peter’s confession in this verse includes "the Son of the living God," which can contradict Luke 9:20 if viewed as a deeper recognition than merely "the Christ of God."
Matthew 16:16: And Simon Peter answered and said, Thou art the Christ, the Son of the living God.
Contradiction with John 7:5
This verse states "For neither did his brethren believe in him," which contrasts with the disciples’ recognition of Jesus as the Christ in Luke 9:20.
John 7:5: For neither did his brethren believe in him.