Contradiction with John 13:38
This verse predicts Peter's denial, while Matthew 26:73 describes the scene leading to it, rather than contradicting it.
John 13:38: Jesus answered him, Wilt thou lay down thy life for my sake? Verily, verily, I say unto thee, The cock shall not crow, till thou hast denied me thrice.
Contradiction with Matthew 16:18
This verse names Peter as the rock on which the Church is built, seemingly conflicting with his actions of denial implied in Matthew 26:73.
Matthew 16:18: And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. [Peter: this name signifies a rock]