The carbon dating was shown to be erroneous, since it was taken from a portion of the edge of the shroud that was repaired from fraying by nuns at that time.
There is other evidence to suggest a far greater age for the shroud, including trace vegetation and the method used to weave the original cloth.
It's Holy Week and, annually at this time, we must have the obligatory "the Shroud is a fake" story. Whether it is or isn't doesn't change the miracle of the risen Christ. Let's not let that fact be overshadowed or clouded by this debate.