Contradiction with John 19:31
It states that Jesus’ legs were not broken, suggesting He was not yet dead which contradicts the request for His body in Matthew 27:58.
John 19:31: The Jews therefore, because it was the preparation, that the bodies should not remain upon the cross on the sabbath day, (for that sabbath day was an high day,) besought Pilate that their legs might be broken, and [that] they might be taken away.
Contradiction with Mark 15:44
It indicates that Pilate was surprised to hear that Jesus was dead already, whereas Matthew 27:58 suggests Joseph requested the body implying Pilate knew He was dead.
Mark 15:44: And Pilate marvelled if he were already dead: and calling [unto him] the centurion, he asked him whether he had been any while dead.
Contradiction with Luke 23:52
It states that Joseph went to Pilate and begged for Jesus' body, similar to Matthew 27:58 but does not mention that Pilate confirmed Jesus' death first.
Luke 23:52: This [man] went unto Pilate, and begged the body of Jesus.
Contradiction with Acts 13:29
It mentions that they took Jesus down from the tree and laid him in a sepulchre, contradicting Matthew 27:58 by differing in who took Jesus' body, implying it wasn't Joseph who requested the body exclusively.
Acts 13:29: And when they had fulfilled all that was written of him, they took [him] down from the tree, and laid [him] in a sepulchre.