This review contains spoilers.
I was surprised to find that this episode was held in such low regard by other reviewers, as personally I really like this one. (But I suppose that's part of 'Star Trek's appeal – there are different stories that appeal to different people; something for everybody).
Much of what I love about this episode is it's quirky nature; the people living as if they were from the 1900s, with strange speech patterns and, of course, 'The Festival'. Such quirkiness could just as easily come from classic British 1960s series such as 'The Prisoner' or 'The Avengers'.
In particular, the scene where everybody is acting pleasantly, the suddenly the clock strikes twelve and everybody starts going crazy, could easily have been an opening teaser for 'The Avengers'.
The Festival itself is never fully explained; partly that's a shame, but partly it adds to its weirdness. I suppose it can ultimately be put down to the misguided rule of Landru.
The episode also has elements of other things I like – a cult (Landru's followers), and even zombies (as the 'hypnotised' civilians slowly march towards Kirk and co., in one of my favourite 'Star Trek' scenes).
The concept of beings being governed by a misguided computer would be used a number of times again in 'Star Trek' and it's later various spin-offs; there are even vague traces of it in 'Star Trek: The Motion Picture' (1979). (If that film had had more of the intrigue of this episode, I think it would have fared much better.)
If there is anything wrong with this episode, it is that the later stages are a bit too talky and dragged out; the last act or so could have easily been slimmed down.
But all-in-all, unlike many, I really like this episode. It has quirkiness and mystery too it, and is a great tale in my opinion. Others will disagree.