But what's most lacking in these shows, compared to the first two seasons, is humor. Even an excellent episode like "Spectre of the Gun" has Kirk too formally addressing Spock as "Science Officer" in the opening scene. Just feels wrong.
I get the impression, since this was the first episode of the season filmed, that certain phrases were used to "clarify" a few roles to anyone new, in the event it was aired first (Likely? Not likely? No idea). Spock as "science officer" (twice in the that scene) and calling the phasers "phaser guns" like they were by Bailey in "The Corbomite Maneuver." Uhura, Chekov and Spock all had dialog to showcase their backgrounds (well placed to display the Mekotian telepathy). Actually, the whole teaser is a mass of exposition for new folks, but the "first contact" introduction helps mask some of it.
Kirk: This is Captain James T. Kirk of the starship Enterprise, representing the United Federation of Planets.
Now we know who Kirk is and who he works for and on what ship.
Then we get this...
Kirk: Lieutenant Uhura, advise Doctor McCoy and Engineer Scott to meet me in the transporter room.
Now we know who McCoy and Scotty are (but not why they're essential to the mission - which they really shouldn't be) and a minute later, we know Scotty is in charge of the transporter and McCoy is cranky about the machine. Imagine you're seeing the show for the first time. You're pretty much up to speed on the basics of the format and the key players. The rest you can get along the way.
So, in that context, I can see why Kirk addressed Spock so formally.