Why Castle Nut on Vert Stab & Rear Spar attach?
 

Why are Castle nuts used on Vert Stab and rear wing spar attach points?

I am following the plans but trying to understand why a standard Nylon lock nut is not used? Is there some type movement between these mating parts?

Self Locking nuts are not used where rotation of the joint is possible. The wing can flex up and down in flight depending on weight of the aircraft and load on the wing. This can over time, loosen the rear spar nut.

Yes you have self locking nuts called out on some of the control bellcranks. The location of these self locking nuts are where bearings are used and the bearing take the rotation and not the bolt - nut.

The fasteners you mentioned can be subject to rotation (as Gary already mentioned).
We often think of bolted assemblies on aircraft to be entirely static but they can move under certain load conditions.

For example - Under high G's, wing tips can deflect up to 1.5 inches or more depending on load and model. If the wing is deflecting, there would be a very slight movement at the rear spar clevis joint, so a castelated nut and cotter pin is used.

Is that true for the Vertical Stab attach points as well? That was also part of the original question. Mine was assembled with Nylock nuts, I didn't even think to question it when I saw them...

Vert. attached with AN365 lock nuts per DWG27A.

On the -10, it is a AN-310 castle nut

That is because the front spar of the vert stab attaches with only a single bolt/nut on the 10, unlike the others which use a grid of 4 bolts. So the flexible structure (the entire vert stab) anchored at a single point needs to be thought of as pivoting minutely around that bolt.

The vertical stab of the 10 is similar in attach method to the main wing, with the difference being the front (instead of aft) spar being the single point used to set sweep/AOA.

that single bolt may protect against structural bending interaction of the horizontal and vertical stab.