I have to say this up front. One thing I didn't care for in TNG was returning characters particularly in the form of Llwaxana Troi. That coupled with characters going back to Earth or Risa whenever they felt like it. It made the galaxy seem small and the ship didn't feel like it was on the frontier.
TOS only did it once with Harry Mudd and it looked like a total coincidence. And I wasn't crazy about the episode he returned either. Having fresh characters helped lend the feeling they weren't hanging around the neighbourhood. And characters weren't going off to Starbase or Earth for leave whenever they felt like it. It's those little things that added to that sense of being "out there."
To that end I hope STC sticks with that sensibility.
Sadly TAS did revisit a number of previous characters and I wish they hadn't. In quite a few cases they were the weaker episodes.
Well, to be fair:
The return of Harry Mudd was intentional. In fact:
According to Walter Koenig, NBC considered making a spin-off series detailing the comical adventures of Harry Mudd after the success of this episode. They assigned Gene Roddenberry to develop the idea, but being busy with Star Trek and other projects, he didn't have time for it, and the series was never conceived.
In "Day of the Dove" they did want to bring back John Colicos as 'Kor' but both times scheduling couldn't be reconciled:
Kor was initially to have appeared in "Day of the Dove"; the writer of that episode, Jerome Bixby, very much wanted to cast John Colicos as the installment's main Klingon character. Colicos was again offered the role and could hardly have been more excited by the prospect of appearing in "Day of the Dove". However, he was unavailable, meanwhile involved in a film being produced in Italy.
But that said, to this day, I really enjoy Michael Ansara's portrayal of the Klingon captain, "Kang".
So, yeah, I don't think Harry Mudd's return was sheer coincidence, and I think had TOS lasted a few more seasons, we might have seen more returning/recurring characters. Honestly, I don't mind it as long as the script/story is good, and with regard t "I Mudd" , IMO - the whole exchange between Kirk/Mudd/Spock about how Mudd ended up on the Android planet is one of the funniest 'played straight' scenes in TOS:
Mudd: "Do you know what the penalty is for fraud on Deneb V?"
Spock: "The convicted party has his choice: death by hanging, death by electrocution, death by phaser..."
Mudd: "I borrowed transportation."
Kirk:" He stole a spacecraft..."
Mudd: "The patrol acted in a hostile manner..."
Kirk: "They fired on him..."
Mudd: "They have no respect for private property! They damaged the bloody spacecraft!..."
Something we wouldn't have gotten if we'd not seen the return of Roger C. Carmel as 'harry Mudd'; so gain, not at all dissappointed they decided to bring him back in Season 2 of TOS myself.