The principles are quite simple. If you don't rotate your lens around the nodal point you end up with parallax error. That is objects that are in the foreground suddenly appear to be in a different spot than objects located in the background. The other issue is lens distortion, because even if you correct for parallax with the correct tripod if you use many of the lenses available you'll end up with barrel or pincushion distortion. Both of these mean your images won't line up.
How field relevant this is depends on your software and the extent of the problems. I show you an example below. In this case I said "Nodal point? I spit on your nodal point!!!" I actually rotated my body shooting handheld. The nodal point was about 25cm behind where it is, and not the 3-6cm a tripod will put you out by.
Here's the result:
Ok I lied. That's not the result it's an interim stack. It shows just how bad the parallax error was in this case. Notice the background is completely unaffected, but the poser in the foreground was made somewhat less pretty?
Well after simply hitting "render" on the software. I get the following result: (I lied again, this result was after a bit of colour correction in photoshop too):
What is actually scary is that this was a 100% perfect stitch when I was done. I did not find a single stitch mark. A few weeks later I shot something from a long way away with zero parallax and there were some frames I simply could not correct for some reason and ended up manually aligning things in Photoshop, which is also an option if your rendering software can't figure out who's supposed to be where in the frame.