AFAIK, the Sacred Sindone (that's how we call here in Italy the Shroud of Turin), is nothing more than a stunning but artificial artifact.
I had the opportunity to view it some years ago (it is occasionally put on display for no more than a couple of months), and as for many old artifacts it has an invaluable fashion and eerie aura, the same you can get from other relics whose authenticity is proven false (like St. James head, on permament display in Amiens), since it makes you wonder how many centuries that artifact has influenced people, how many fought for it.
Apart from the carbon isotope analisys, the Shroud of Turin (as well as other shrouds) has been analysed in almost every way possible, and the majority of the results find the shroud age compatible with the time it's referred to in the chronicles, the 14th century. A very strong point, imho, is that right after the Middle Ages, and later in specific times (like the Counter Reform), there's been a high quantity of relics fabricated for both political (to raise awareness and strenghten the position of the Christian Church), and economic reasons, since relics were fabricated and sold by the Christian Church together with an "authenticity" certificate. I happen to own (I have some high priests as ancestors) many of these "emission certificates" (16-17th century) and one of these relics, that's, supposedly, part of the tip of the sword used for St. James beheading, according to the certificate.
Very interesting, eerie, astonishing artifacts, but even the Shroud fits perfectly the historical scenario of the 14th century, apart from the forensic evidences.