There are at least
some episodes of TOS that it
is important to watch in a particular order for plot reasons, if you want things to make relative sense. This list may not be exhaustive, but here's what I can think of at the moment:
As mentioned by
@Tenacity above, "Mudd's Women" (TOS) should of course be watched before "I, Mudd" (TOS).
"The Naked Time" (TOS) needs to be watched before "Tomorrow Is Yesterday" (TOS), which in turn needs to be watched before "Assignment: Earth" (TOS), to preserve the accidental discovery of time travel via the slingshot/breakway factor method and then the development of its purposeful application.
"Balance Of Terror" (TOS) needs to be watched before "The Deadly Years" (TOS), which needs to be watched before "The
Enterprise Incident" (TOS) to preserve the revelation of the Romulans and their ever-improving cloaking device, and their switch to using Klingon ships.
"What Are Little Girls Made Of?" (TOS) needs to be watched before "Operation -- Annihilate!" (TOS), because in the former we are told Kirk has a living brother named Sam, and in the latter he dies.
"Dagger Of The Mind" (TOS), being the first introduction to the concept of the Vulcan mind meld, should come before "The Return Of The Archons" (TOS) / "A Taste Of Armageddon" (TOS) / "The Changeling" (TOS) / "Mirror, Mirror" (TOS) / "By Any Other Name" (TOS) / "Spectre Of The Gun" (TOS) / "The Paradise Syndrome" (TOS) / "Is There In Truth No Beauty" (TOS) / "Requiem For Methuselah" (TOS) / "Turnabout Intruder" (TOS). Additionally, if it's seen before "Whom Gods Destroy" (TOS), then Kirk's recognition of the modified neural neutralizer has context.
"The Alternative Factor" (TOS) should be watched before "Mirror, Mirror" (TOS), because in the former the concept of a parallel universe is only considered a theoretical possibility at first, whereas main characters directly experience a crossover with one in the latter.
"Errand Of Mercy" (TOS) should be watched before "The Trouble With Tribbles" (TOS) / "A Private Little War" (TOS) / "Day Of The Dove" (TOS), because the latter involve the peace treaty with the Klingons established in the former.
As for the various parallel Earth stories, while there are at least some oddities any which way you slice it, by all rights "Miri" (TOS) really should come first, because everyone is completely astonished at the "impossible" prospect—although it's a
particularly extraordinary example even compared to others, because it isn't merely a similar
society but a full
geographical duplicate. They are aware of a principle called Hodgkin's Law of Parallel Planet development by "Bread And Circuses" (TOS), of which the planet there is cited as "an amazing example," coming complete with spoken English, yet not
quite the "virtually impossible" duplication of period-specific costumes and symbols that call out the Nazi uniforms in "Patterns Of Force" (TOS) as being down to cultural contamination rather than "fantastically slim" chances. "The Omega Glory" (TOS) then takes precisely
that extra step in presenting a "parallel almost too close"—no
almost about, if you ask me—but then thankfully we finally get a potential explanation in "The Paradise Syndrome" (TOS) in the form of the Preservers, who "apparently account for a number of" such cases.
Phew!
-
MMoM