Well, I have a problem with the shroud's supposed authenticity. One only needs to look at the latter part of the 19th chapter of the Gospel of John to see a serious discrepancy with this 'shroud' theory.
JOHN 19: 37-42 NKJV
37 And again another Scripture says, "They shall look on Him whom they pierced." 38 After this, Joseph of Arimathea, being a disciple of Jesus, but secretly, for fear of the Jews, asked Pilate that he might take away the body of Jesus; and Pilate gave him permission. So he came and took the body of Jesus. 39 And Nicodemus, who at first came to Jesus by night, also came, bringing a mixture of myrrh and aloes, about a hundred pounds. 40 Then they took the body of Jesus, and bound it in strips of linen with the spices, as the custom of the Jews is to bury. 41 Now in the place where He was crucified there was a garden, and in the garden a new tomb in which no one had yet been laid. 42 So there they laid Jesus, because of the Jews' Preparation Day, for the tomb was nearby.
Jesus was wrapped up like a mummy according to this Scripture. With the application of the myrrh and other spices and substances, Jesus was entombed in a gummy shellac shell of a cocoon. Something is not quite right with the shroud as the purported burial cloth of Jesus. It just doesn't jibe with the Scriptures.