The Star Trek Continues followup was interesting.
It definitely was, and seeing how the Mirror Universe continued on its own after the events of the episode was not only fascinating, it also supported my (not particularly well-developed) idea that the two universes would now diverge because of the inflection point of the unexpected exchange of four of its members for four of another universe.
In a way, they did. "Yesteryear."
"Mirror, Mirror" is essentially an alternate history story. "Yesteryear" is a "sequel" to "The City On The Edge of Forever." Both of those stories invoke paradoxes, while "Mirror, Mirror" is multiverse. Still, I see all of them as fantasy with very flimsy logic. With such a radically different back history, how could a Kirk and all the other characters converge on an MU Enterprise to make the story work?
Enh, that just doesn't really bother me that much. There are obviously differences in the universes, but basically you're asking how Kirk, Spock, McCoy, Scotty, Sulu, Uhura, Chekov and Kyle could both be on the Mirror Enterprise and "our" Enterprise despite the Mirror Universe's radically different conditions. (I believe those are the only characters in common to both universes that we encounter until the end of the episode when Moreau appears on our Enterprise. I mean, of course they used some of the same extras, but they could have had different names and such, a phenomenon that happened often enough in "our" universe throughout the series' run, and whether they intended it or not, they seem to have avoided using the most familiar or most obvious S2 extras like Leslie, Hadley, Brent, etc.)
I guess I just don't find it that hard to believe that those eight characters could all be in roughly the same positions - and not exact positions, given Sulu's job switch - on the Mirror Enterprise. I'm reminded of Spock's eddies and currents in time theory from "City on the Edge of Forever." Perhaps the two universes exerted a pull on one another that caused those characters to be drawn to one another in both. And we see from Moreau's introduction on "our" Enterprise at the end of the episode that she obviously didn't follow the same path as her counterpart.
The best Star Trek episodes and movies sometimes catch that figurative "lightning in a bottle." The stories may not totally work logically and the plot holes are many, yet put together, the end result is magical. You put aside the questions and just enjoy the experience.
This is one of those. "The Wrath of Khan" is another.
My go-to example for that is "Space Seed," as I've said many times in many threads. It has massive, massive, galaxy-sized plot holes, most of them centering on the familiar defects in shipboard security, but it is a wonderful episode nonetheless, and worked well enough to serve as Meyer and Bennett's selection as the basis for Star Trek II.
