The problem here was hinted at in the first tutorial, where we're initially copying and pasting the images from the tiff file. "Try to eyeball the largest of the three images." Well why aren't they all the same size? They're all of the same subject....
If you go back to the channels window and click alternately on the blue and green channels, you can see that in this particular image, blue is rotated slightly clockwise with regard to green. However, we're not just dealing with an angle in one axis, we're dealing with a three-dimensional skew.
 Green |  Blue is skewed |  Could be worse |
How did this happen? Some distortion could theoretically be due to a bad "angle of attack" in the LOC's scanning routine, but this doesn't really explain the phenomenon, because such distortion would be uniform on all three images. I think the most likely explanation is a minute discrepancy in the placement of the internal camera mirrors that I assume were used to split the image into three parts.
It helps to be philosophical, I think; perfection is not a part of the world we live in, and no matter how much we dink around with our Photoshop images they will never be "perfect." All we can do is the best we can, and obviously we have not yet arrived there with this particular project.
By adopting this outlook, we can forgive the fact that the problem lies in the method of photography used. Think of poor Sergei Prokudin-Gorskii, barely out of the nineteenth century, constructing a camera that takes crisp, detailed color photographs using only black and white film! Surely he too saw the futility of achieving perfection on this Earth. Constructing such a device can't be an easy thing; you try it—the task is beyond my capabilities (and at any rate I already own a digital). So slight mistakes were made, and sadly, we've gone and magnified them.
And have we ever magnified them! Each image on the actual negative plates has a width of about three inches. We've got a target print size of almost four times that, and have additionally magnified the image 300% beyond. Not only that, the necessary adjustments often amount to mere fractions of a degree of angle. Kind of puts things in perspective; short of lottery-winning odds, Prokudin-Gorskii had the angles pretty dead-on.