The question for me then becomes, how on earth do you enjoy anything?
I enjoy lots of things. Having high standards doesn't get in the way of that. Sturgeon's Law applies, of course, but the remaining ten percent is worth holding out for.
Any work of fiction inherently will contain some inconsistency at some point along the line, that's unavoidable, it's part of the definition.
I don't agree with that. Inherent? Part of the definition? How do you figure?
That said, even to the extent that various otherwise good works do contain logical contradictions, it's necessarily a matter of degree, not of kind. It's not all or nothing. An inconsistency about some obscure bit of trivia that's not really relevant to the plot or characters, or one that was genuinely unavoidable for (reasons), or one that's only seemingly dissonant but can be rationalized away with a little logical inference, is a lot easier to swallow. On the other hand, an inconsistency about something major, obvious, and/or central to the story, one that's committed as a matter of choice and could have been avoided, and/or one that has no readily available explanation, or even that eschews explanations that are available in the narrative context...
...like, for instance, completely changing the look of the Klingons, their ships, and everything else about them, in a story where Klingons are central, in complete defiance of almost everything previously established about them including a retcon in the last series that could have been used to explain varying appearances and/or internal dissension, for no apparent reason other than "somebody in charge felt like it"...
...something like
that yanks me out of a story.
Trek in particular is notably riddled with them, infamous for it in fact, so why torture yourself by looking so closely for something you know will bother you?
I wouldn't say Trek is "infamous" for it. On the contrary, as I've posted before, I think Trek continuity hangs together far
better than that of most other TV properties... certainly compared to others originating in the 1960s and/or others with hundreds of episodes behind them.
Regardless, though, I'm hardly "torturing myself by looking so closely." I'm talking about stuff that
jumps out at me. I couldn't avoid noticing it if I wanted to.