As revcollector said, it's the paper that gives it away. The paper grain orientation noted in the Pictorial series re-issues also applies to the 1861 series re-issue. This is a simple, objective way to differentiate special printings from the normal printing
in most circumstances. (I have to qualify my statement because there is a regular issue #68 that is on a similar grain orientation, but the color has a lot of yellow and the impression is fuzzy.)
The NBNC re-issues are printed on paper with a grain oriented horizontally. Shrinkage, being across the grain, compresses the design vertically.

This is an image of the #106, upon which I have superimposed a sliver from the #68 on the far right so you can see the #106 is a bit shorter. Obviously, high-def scans are immensly helpful in seeing this tiny difference.

This is the #106 with a strip of the #68 laid across the top. Note the #106 is wider than the #68. The grain of the #68 paper runs vertically so shrinkage is horizontal, compressing the design width.
The subjective test I use for this specific denomination is the clarity of Washington's right-hand wig lock (our left) and the crosshatching in the vignette in the same area. When I see a clean crosshatching in this area it's a signal to me that it's probably a re-issue, which I can verify using the design size criteria.
Ray, your observation of Washington's beady eyes on the re-issue is spot on.
Thanks so much for everyone's comments, and please let me know if you have information or made observations that differ in any way from what I have posted. I don't want to mislead anyone, but I have come across several re-issues utilizing this knowledge, so it should help others in the hunt.