The "guy with eyepatch" is a subtle an indirect nod to General Chang for those who see the reference, but the scene can also be perceived in enough ways by audiences regardless of familiarity with the show and it's very deftly done. True, knowing enough of the show and episodes does help with a lot of the humor being used as an added bonus but in most instances it's not needed and it still feels like its own thing first and foremost. I love this. The show uses a lot of these moments (so did the theme) and it's done impeccably well. The show is a comedy, is a parody, anyone thinking this is going to be a serious outing is going to not enjoy the show and I'll get back to that in a tic. They makes these "callbacks" their own elements in stories instead of just being a 2D "hey look we're taking this the old show as a joke so go 'ha-ha' now." It's really VERY nicely handled, very nicely done.
A more generic joke, I loved the setup for the spider thing that Boemler falls into. They mention what the spider does, he falls into it, then they make the dirty joke. And I was in stitches. That's how to do it - subtle and dirty yet innocent at the same time and letting the audience see if if's funny and if so why and on their own perception rather than being told outright. This is also why "you are out of your vulcan mind" works whereas "you are out of your fucking mind" does not - noting this can be done in any genre, comedic or otherwise. This show gets it, it understands, it RULES.
Yes, this show is a comedy - it's risky to do, especially when they're using a new premise in the franchise of exploring "second contact". "Second contact" is brilliant in of itself, and trying comedy (a risky and subjective genre to begin with) is risky but if it pays off it's gold. This is gold. IMHO. Those who disagree just don't like the combination. It's subjective. Nothing wrong with that.
The story's most prominent universal moral is to not jump to conclusions. Raise your hand if you're good at that because many of us humans do.
Another moral theme, albeit a relative one, is using what TOS movies did and show characters snub authority if there's a good reason, which the episode states involving the local farmers Mariner helps out (and who are grateful and not trying to do anything rotten in return - score another plus for this show. Helping others also seems closer to a universal moral but there's also a time and place for the whole of the issue and this episode explores it and in a non-cynical way. It was fantastic.)
Note that Mariner too has her own foibles and issues, all the characters do. They are all types I'm finding likable, even with the foibles. That's big. IMHO, YMMV. They all also misunderstand that bridge crews are for the most part not all out for glory and that was an interesting line (did the TNG episode of the same name make any such quips? I don't remember but it's a moot point and a point good enough to bring back anyway.) This show, at least this episode, is showing a level of maturity that's incredibly understated.