I'm getting behind here...
Ray Schneider's paper attempts to discredit the radiocarbon dating in three ways; first by examining the irregularity in the Nature paper itself, then by looking at three images of the radiocarbon area, and finally by correlating various gradients in those images with the different radiocarbon ages. In some cases his primary observations are correct, and in others false or deceptive, and in no case are his conclusions justified.
1) The Nature paper very properly calls attention to the circumstance that as reported by the laboratories, there is only a 1 in 20 chance that the three dates refer to the same piece of cloth. However, that does not mean that they need be rejected out of hand. An analogy may help. If a farmer sends three men to count the sheep in a field, and they return with 70, 72 and 65 (allowing for a sheep or two either way for miscounting), these numbers do not apparently concur. So what to do? Abandon the information altogether, or suspect that maybe the precision (a sheep or two either way) was not as great as suggested. Could there in fact be 250 sheep in the field? Or 14? Probably not. Making the best of a messy job, the farmer assumes that the counters were not as precise as they claimed, and makes an appropriate adjustment - maybe between 60 and 75. Probably not more or fewer. This is exactly what the Nature authors did. It is wholly untrue that the results are meaningless.
2) The Quad Mosaic photo (false coloured) shows a largely yellow and orange shroud, with a green corner which Schneider attributes to a different material. This is somewhat disingenuous, as this is only one quarter of a much larger photo. There are four of these Quad Mosaics covering the full length of the Shroud, and every one has a green corner. More importantly, every one also has a bright blue band across the top half. If the bottom left hand corners are indeed of a different material from the rest of the Shroud, then so are the four bright blue bands which cross the whole width of the material. A reductio ad absurdam, I think.
3) The next photo pretends to be a UV photo taken by Vernon Miller in 1978. Miller's photography is well detailed in his paper in the Journal of Biological Photography, and this photo does not even remotely resemble any of his. It is not a UV photo, and has curiously had the 'missing corner' section cropped away. I do not know its provenance.
4) Finally, we have another false colour photo, also in yellow and green, which purports, as before, to demonstrate that the different colours represent different materials. Although in this case, the 'missing corner', in the form of the backing cloth, is present. Sadly for the hypothesis, the part of the backing cloth which had been covered with the Raes section is bright white, showing that the colours do not represent different material at all.
5) Be that as it may, the end of the paper shows a couple of graphs. The first one shows, correctly, that the sample furthest from the edge of the Shroud (Arizona) produced the youngest age, and the sample closest to the edge of the Shroud (Oxford) produced the oldest. This in itself is odd, as it suggests that the edge of the Shroud is less contaminated than the interior, but it is also in direct contradiction with the following graph, which instead of showing an inversely proportional relationship between the alleged contamination and the age (the more the contamination, the less the age) in fact shows exactly the opposite (the more the contamination, the more the age). If there is any truth in these images, they show that any contamination of the Shroud had the effect of making it appear older than it really is, not younger.
So, although a paper produced by a professor of Mathematics may at first sight appear reasonable, a detailed study of it shows that his conclusions are not only based on faulty evidence, but even if taken as true, that the evidence in fact shows exactly the opposite of what was hypothesised.