NBC was the "full color network" at the time I believe, ABC and CBS were still in transition. And it was still owned by RCA possibly, and Star Trek often showed up in RCA television set print advertising.
There's definitely a glitch in the Matrix with Kirk entering the room he's already in while Uhura holds a phaser on Klingon Marlena.
Curly: Moe, Larry, the cheese! Moe, Larry, the cheese! (Horses Collars, 1935)