I can't imagine that a professional actor such as Nimoy would look in the direction of the camera without the approval of or instructions from the director. Ergo, Nimoy may have been directed to do that, to give the audience a knowing glance, Vulcan style. I read it as a theatrical technique to draw the audience in; a lot of blocking in TOS had the actors facing the audience as if in a play. Characters would face the same direction and talk to the audience when to be totally in character they would have faced each other. This is probably really just one of those theatrical tropes.
Another subtlety that TOS-R incompetently obliterates is that the ship orbits the planet in the opposite direction for the whole episode: all the stock footage for planet orbit was reversed as a mirror reflection. With Alice in Wonderland, the whole episode was intended to break the mold of the normal Star Trek episode, up to that time. The whole scene with Kirk getting his back scratched on the bridge is an outlier to begin with.
Another subtlety that TOS-R incompetently obliterates is that the ship orbits the planet in the opposite direction for the whole episode: all the stock footage for planet orbit was reversed as a mirror reflection. With Alice in Wonderland, the whole episode was intended to break the mold of the normal Star Trek episode, up to that time. The whole scene with Kirk getting his back scratched on the bridge is an outlier to begin with.
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