It carbon dates to about the time of the fire that nearly destroyed it. That is odd, since it had been there for some time before the fire. If carbon dating was completely reliable, which it has been proven not to be, then its daing would be certain, but I would not want to rest my entire argument on one factor alone for dating the shroud. The weave and composition of the fabric, as well as the pollen embedded within the fabric of the shroud are consistent with fabric from Israel at the time of Christ, so there is a reasonable argument in favor of much greater age for the shroud than carbon dating would indicate.
The real question about the shroud should rest on whether or not it is an authentic burial shroud. If it is authentic, then it is the shroud of Christ. It portrays a man crucified, scourged, and wounded about the brow in multiple places consistent with injury sustained by a crown of thorns, and wounded in the side. If it an authentic burial shroud, it is Christ's. If it is not an authentic burial shroud, then it is a fake.
The priests who risked their lives to save it from the fire must have believed it to be a holy relic. The burns are the result of molten metal from the small casket that contained it dripping onto the shroud during the fire. It is unbelievable that they entered the fire to retrieve it from that heat if they thought it was a fake... after all, they could fake it agiain, and then claim that it had miraculously survived. But before we "bandwagon" the notion, think again. If it is an authentic burial shroud then that's not what happened.
Ultimately, this issue is so polarized, because most people realize that this is one way evidence. If it is faked, it says nothing about the authenticity of the record of the crucifixion. It only points to a religious zealot who went overboard, or more likely, a charlatan who profited by faking the shroud and selling it as authentic. But if it is the shroud of Christ, then it is physical evidence that the details of the crucifixion story in the Bible are true, and then the empty shroud becomes a fact that unbelievers must deal with.