The first episode was "Miri", in which the Enterprise discovers a planet identical to the Earth - probably so that the inhabitants will speak English (the "Earth" language, I guess) and to enable Dr. McCoy to make sarcastic cracks about the architecture of the studio backlot - except that all the adults are dead and the children are aging very slowly, until they reach puberty, at which point they contract the disease that the adults had and die too. I picked this episode because it stars Michael J. Pollard (then about 27) and Kim Darby (then about 19) as the chief purported pre-adolescents.
The other was "Mudd's Women," which I picked for its colorful guest star Roger C. Carmel. Other than that, you don't want to know about this episode. You really don't.
I found that the acting, though sometimes over the top, particularly from Shatner, is mostly pretty good. Even the plotline whereby Darby, as the eponymous Miri, falls in love with Kirk but the Hays Code keeps them apart, while boring is not wincingly bad.
The problem with the show is its pacing. The plots grind to a halt and keep spinning in place, occupying time so that the story won't end before the episode does, or move glacially. Repetitious, self-congratulatory dialogue such as this doesn't help (actual example):
SPOCK: According to their life prolongation plan, what they thought they were accomplishing, a person would age only one month for every one hundred years of real time.In "Miri," the party of top officers, plus a couple of anonymous redshirts (their only name is "guards") who, surprisingly, don't get killed, is stuck without any way to evaluate their vaccine to stop the adult-killing virus from which they're all now suffering, and the reason they have no way to evaluate it is because they have no contact with the ship's computers, and the reason they have no contact with the ship's computers is because the elusive children taunted them all into rushing out of their lab in search of said children, and then while they were out Michael J. Pollard - who'd expected them to do this - snuck in and stole all the communicators which they'd stupidly left sitting out on the tables.
JANICE RAND: One hundred years and only one month?
SPOCK: Exactly, Yeoman.
Insert, in a desperate attempt to get the communicators back, William Shatner in the Speech Least Likely To Persuade A Group of Wilful Kids to Do What You Want.
So Dr. McCoy gets tired of waiting and injects himself with the vaccine, without knowing what the dose should be, and when it cures him instead of kills him they know it's OK. This is a vaccine, mind you. Vaccines are supposed to prevent not cure ... oh never mind.
One thing that interested me, because it's something I've never seen discussed in a half-century of Trek trivia, is that when the top officers depart, they leave the com in the hands of a lieutenant named Farrell, who also plays a secondary role in "Mudd's Women." Had you ever heard of this guy? You will find him listed in sufficiently detailed Trek catalogs, but he seems to play no role in the mythology. I seem to recall that, in later years, only big-name characters could take the com, that if everybody else was gone then Scotty had to be on the bridge, even though he'd be better off in the engine room fretting about the dilithium crystals which is what he does in "Mudd's Women." I prefer the acknowledgement that there's a whole lot of crew members on the Enterprise besides the ones we know.