Don't overthink it. The writers didn't. Nor should they have.
On a philosophical level, some of the sci-fi/fantasy ideas should and do get some flexibility regarding inconsistencies and just accepted by the audience. Especially if the episode remains engaging and succeeds with its biggest points, the nitpicks seem far less prominent.
"The Enemy Within" was never about the technology, that was just a springboard and means for the psychoanalysis and suspense-driven horror (a la
Twilight Zone) - neither was it overblown nor swept under the rug. But at least they acknowledge and use consistently the cause of the problem for its solution. Does "Mirror, Mirror" flow as convincingly in this regard? Indeed, would it have been better if Kirk and crew woke up in Sickbay where Chapel informed them the transporters were rendered inoperative so the crew were recovered via shuttle craft and are now recovering -- during which it was just Kirk having a little dream. Which actually makes sense, given one of Marlena's comments, teehee... (As well as being an early example of the "it was just a dream" trope. Or an unintentional callback to what "The Wizard of Oz" did.) Plus it'd be a fun poke at "The Enemy Within" having to pretend they had no shuttlecraft at all in order to keep the drama for the grounded crew going. (In real life, if memory serves, they were scrambling for the means to get the craft built and it wasn't ready, and they had to get stories completed to film and get aired. The result? Look the other way, put fingers in ears, and say "La-la-la and I also coughed". But unlike for early season 1, season 2 didn't have that hindrance. They didn't need to make a contrivance to later skate around.)
I'll agree that overthinking when watching can be a problem (been there, done that a few thousand million times - true). But just whizzing out any old script "because plot" can be just as much rubbish, if not more so. The more mental gymnastics become needed to justify the situations in "Mirror, Mirror" can and will take the audience out of the story or scene it's supposed to remain engrossed in. The audience is being asked a lot for this story: Outfits magically change with new bits added or removed. The cause is a freak storm during simultaneous exchange except all of a sudden they have to just get to the transporter room before the ion storm ends and for no reason it no longer matters where their opposites are - one can potentially headcanon around the storm and the coincidence of their counterparts beaming, but the minutiae with their clothes and shiny new weapons? Let's throw out the "simultaneous exchange" as the story seemed to have done that by the end as well, and if it were a factor then surely they'd beam back wearing the wrong outfits and/or end up in the brig. Pre-DS9, the crew only having their spirits transposed could arguably be made to work... Good sci-fi doesn't need to address everything, but great sci-fi keeps enough plot coherence and without spoonfeeding all the minutiae at the same time, since the plot coherence makes it easy for the audience to resolve any loopholes or issues on their own. It's been a while since I've seen it, but I never got the impression "Mirror, Mirror" even tried after the second act. Maybe they were running out of time as much as our crew were.
To go even one step further: The story also - and ironically - treats the viewers as a gaggle of ninnies with the "Tantalus Field". First, let's put to the side how "Tantalus" was the rehabilitation hospital colony for criminals in "Daggar of the Mind", as now that begs some genuinely cool questions about how nasty the mirror universe was, assuming that was the intent. But it also just describes a throwaway maguffin used to take care of the
Batman villain cartoon goons mirror universe conspirators in a quick bit of fisticuff-focused shlock. Oh, and it does so all while leaving Sulu alone to be knocked unconscious because...
someone decided that if they saw red shirt Sulu magically disappear they'd think our prime universe Sulu would as well?! There is zero reason why Marlena wouldn't have popped him out of his world as much as the rest of them because she's on Team Kirk, at least when not oiling her traps with that dialogue that somehow swooshed so far over the censors, oddly... (1000 bonus Quatloos if you were anticipating my returning to one-liner.

) At least they didn't have his buddies having wordy iron-on decals pressed onto their shirts like what Batman 66 did every week, so it could have been worse. Indeed, even bad-universe Uhura got to show her navel, so the censors who otherwise never let anyone show theirs understood the difference on a contextual level they could relate to. Well, possibly anyway, it'd be fun to be a fly on the wall in the script proofreading room circa sixty-seven. I once saw a fly on a wall, so I asked it if it knew English. It just started, then buzzed toward the cats' litter box. That's the most I'll ever get to time traveling to 1967 after not using
Dr Seth Brundle's device. Plus, the 1986 remake of "The Fly" is an early example of how a reboot/reimagining can actually be as effective or better than its progenitor. Loved it and the 1958 original, but I flygress...
Even then, rolling along with what begs fair and reasonable questions, there is a great story to be had in "Mirror, Mirror" - even if it piggybacks on the themes of "The Enemy Within" but then applies a wider gamut via multiple people from a different dimension. Fast forward a few decades and it becomes a playpen for increasingly overdone fanwank -- never cared for it in DS9, though where DSC seemed to go with it (too early on or not), had something in its favor with Lorca.
All that said and I am known for word salad buffets with delicious vinaigrette, for what the 1967 original story did, nothing else in Trek comes close in terms of the story
as a whole and there's both fun and ideas to be had. But even then, the 1967 isn't without a fair amount of valid nitpicks. Overlook those and the story has its rewards when not reveling in the shlock.
And now I have it penciled in for viewing, as I want to be in full nurd mode to see what I may have missed the last time I saw "Mirror, Mirror". The answers might be there and I misperceived. Or they never were and was driven more by contrivances than "The Enemy Within" ever could. Nitpicks aside, I do enjoy both stories and are very worthy examples of TOS. The latter became quite famous and iconic, so it's not
bad!
