Writers craft screenplays for an episode that airs in less than 60 minutes and then is done. Maybe it'll appear in syndication, or maybe not. If it does, who knows how long. There's pressure to get a story out and filmed. They don't have the time or incentive to neatly tie up every little bit of information. We need to appreciate that, rather than scrutinizing an episode as if it were a book to be referenced for all time.
That said... it is interesting to discuss the holes/gaps/flaws and find ways to explain things so that they make sense. To a degree... we can go about stretching things so far, which then makes things begin to look ridiculous.
In "The Enemy Within", the shuttlecraft didn't appear yet. There was an intention to have one, as certainly the ship was designed with a hangar deck prominently in the aft section of the secondary hull. But as such, the only way people were getting on/off planets was via transporters. That's the main reason why we don't hear any proposal of using a shuttlecraft. We can easily explain it away as the weather was too rough in that whole area... But anyway, this was the first hole raised and I don't intend to restart conversation on it again.
The "Wink of an Eye" episode was terribly fraught with mistakes and ambiguity. The whole idea of being accelerated isn't explained much with respect to lifespan. The only thing we learn is that when "newly accelerated", any cell damage causes you to age rapidly. There were inferences that people introduced to the Scalosian acceleration don't last very long, that "life will be brief." We don't know if that's just a few months or a few years. The Scalosians seem to have a different kind of lifespan. Given how they're in an accelerated rate, you'd think they'd grow old and die in short order... but they don't. I do agree that Kirk didn't do the right thing... with the antidote, the Scalosians could be converted back to normal. The main issue for them was male infertility. Certainly some solution could have been found for them. But in the end... I think the real problem was the 50 minute barrier. There wasn't enough time to explore this.
With regard to command competency, there's a bit of ambiguity regarding Kirk in
The Enemy Within. He has been split in two, but his "civil" side is the one that is commanding. He has trouble being assertive, but can make logical decisions. When it does come down to the point of relieving him, somehow he does muster some assertiveness. He uses his intellect to overcome the obstacle. It's not enough of an issue that would require relieving him.
In
Obsession, Kirk is basically faced with conflicting priorities: a) deliver much needed perishable medical supplies or b) contain/eliminate a powerful creature capable of quickly killing people. Realistically speaking, Kirk could have deployed a probe to keep watch of the planet, to monitor if and when the creature might leave it, then go on to deal with the other mission. But that wouldn't make for an interesting story.

Speaking of which, at a later point Spock says there's evidence the creature is ready to "spawn." Spawn? It's a gaseous cloud. A creature unlike anything they've ever seen. How could he know this? I guess we'd have to assume that the energy composition reoriented in such a fashion that Spock concluded it was preparing for fission.