I know about the fanzines and once I discovered Starlog had Trek in it, it was on my "must see" list, but we didn't talk continuity or even squabble over the characters much, other than the "Kirk > Spock, Spock > Kirk" type arguments that young teens had.
Part of this was that even in syndication, the show was "live" and one couldn't pause and rewind to catch a mistake.
Honestly, we just enjoyed the show for what it was. I was more interested in the story - was it entertaining? Was it compelling? - than I was in the ship or details that some fans perhaps obsess over more than I would. I chalk that up to being a female fan back then - it was more about the feels than the fact that they got xyz wrong or about ship details.
I'm still more interested in the story. We've had so much Trek now that there are contradictions as well as stuff that is disliked, so I just make my own head canon anyhow. TBH I don't notice most boo-boos 'til they're pointed out. I guess I'm not observant.
P.S. Team Spock. Kirk looked too much like my father back then and one can't crush on one's father. Plus - Spock appealed to those on the fringes and who is more on the fringes than young teenagers - caught between two worlds.