I am watching "Where No Man Has Gone Before" (1.03) and have noticed something that later Star Trek shows such as Star Trek: Voyager contradicts. At one point pretty early in the episode, Kirk instructs Mitchell to leave the galaxy at warp factor one. Later shows clearly indicate that leaving the galaxy would not be possible (not even at warp factor ten let alone at warp factor one). The whole premise of Star Trek: Voyager, for example, is that the crew gets stranded in a different quadrant of the galaxy, and the journey home is expected to take about seventy-five years. I am sure that there are other instances of this kind of writing error happening throughout the franchise, as well, but I am pointing this one out because I just caught it. It's so frustrating that the writers weren't more careful than that.
Could it be that maybe the galaxy they are talking about in Where No Man Has Gone Before be just the one they are in? Galaxies are numerous in the universe, whereas Voyager got stranded in a different quadrant, not galaxy.