There were some exceptionally interesting adventures during TOS that beg for a follow-up:
"The Menagerie" is where it all began, with "The Cage". I can't think of a better place to revisit! What happened to Pike and Vina? What happened to the natives of Talos IV and their "zoo specimens"? Did the Talosians find a way to survive? What if another spacecraft encountered Talos, and stirred things up again, causing Starfleet to send Enterprise to straighten things out?
"A Taste of Armageddon" showed the Enterprise getting caught between two warring planets that apparently possessed technology that was roughly on-par with the TOS-era Federation. It would be great to see if Ambassador Fox had to recall the Starship Enterprise because the process of reconciliation turned out to be a "mighty rough ride".
"A Private Little War" showed us a primitive society being exploited by the Cold War rivalry between the Federation and Klingons. It would be interesting if Starfleet ordered the Enterprise to find a way to curtail the Klingon interference on Neural to avoid prolonged involvement there, and to see Kirk wrestle with the moral dilemma of seeing his hillbilly friend Tyree suffer from the continued conflict, possibly getting killed as well, while still having "a job to do". Can the Enterprise crew figure out a way to make Neural more trouble than it's worth for the Klingons, or will the Neuralese wind up being plunged into endless warfare?
"Bread and Circuses" showed us a 20th-century-like society, whose leadership possessed knowledge of the Federation, starships, and the Prime Directive. Not only is this an embarrassment to Starfleet; it could pose a long-term security issue as the people of Planet IV, System 892 continue to advance, possibly into space. And what if other aliens visit this world, and meddle with its culture? Or, perhaps of greater concern, what if a Federation (or allied) spacecraft were to crash-land on this planet, and the wreckage and survivors were to be captured by the natives? Would Starfleet have to send the Enterprise back to rescue the survivors and destroy any recovered technology? What would Proconsul Claudius Marcus do with these people? Would he interrogate them? Would he hold them hostage? Would he treat them as honored guests to see what he could get out of them? And if Kirk returned to rescue the survivors, would the Proconsul "respect" the starship captain, or try to assassinate him? What if hostile aliens landed on the planet and tried to establish relations with the Proconsul? (Klingons, Romulans, Gorn, or others) This episode opened up many possibilities.
In "Is There In Truth No Beauty?", we are introduced to the mysterious and enigmatic Medusans and the equally unpredictable Dr. Jones. The Enterprise also discovered the hitherto unknown time continuum that leads to some mysterious far-off place. This screams for a sequel, as Starfleet will no doubt wish to explore this continuum, determine the location of the "unknown void", and try to figure out how extra-galactic travel like this works.
"The Tholian Web" must be one of the most poorly interpreted original episodes for sequels. While "In a Mirror, Darkly" is lots of fun to watch, its foundation of Tholian intrigue undermines the premise of "The Tholian Web"; there was no evidence of foul play in the demise of the Starship Defiant. In fact, the basis of the story seemed to be to show the Enterprise crew trying to cope in a region of space where conventional science and technology doesn't operate as it should. Spock, Scott and McCoy were forced to "think outside the box", like NASA did in APOLLO 13. While it would be interesting to see the Enterprise try to deal diplomatically with the Tholians, it would be much more interesting to see Enterprise try to re-enter the "no man's land" to analyze the fabric of space there for future exploration and survival training, and possibly to seek out and recover the lost Defiant. I just can't see the TOS Federation letting a fully intact starship drift away like that when Spock obviously found a way to fly the Enterprise to safety.
