Built on a strong premise in the same vein as Invasion of the Body Snatchers (1956) and featuring some fine acting from Nimoy, the faults of this episode lie in the teleplay and the mismanaged budget.
Like "Devil in the Dark", the episode takes a creative approach to its alien nemesis, this time inventing a creature that lives through scattered brain cells that attack humanoids, forcing them to carry out the creature's will and enabling the cells to hop from planet to planet. It's a great science fiction/horror idea, because it highlights an alien being but lets the humans do the acting.
Unfortunately, it also requires the budget to pull it off, with alien brain cell props and extras needed to drive the concept. Carabatsos's teleplay tries to make an end run around the issue by limiting the number of people who appear on screen and tries to make it more personal to Kirk by having his family infected. The result is that much of the episode involves people lying in sick bay fighting pain instead of angry mobs running amok.
It doesn't help that each of the cells look so fake that even one of the crew members observes, "It doesn't even look (The episode becoming self aware might be a cute moment, but it doesn't solve the problem that the alien simply isn't believable).
The climax is doubly poor for including a false sense of urgency (with no need for Kirk to push McCoy forward so quickly with his tests) and false consequences to drive the drama. To top it all off, because the episode was running long in the editing room, they don't include a scene that ties up the plot line involving Kirk's family. (Sadly, the actor who plays Kirk's nephew, Craig Hundley, does return for third season's "And the Children Shall Lead", an entire episode that should have ended up on the cutting room floor).
Despite its flaws, however, the "Operation" still works in a way. The idea behind the story serves as a strong enough backbone to keep things interesting, and Nimoy gives a suitable performance as character attempting to work through pain with quiet dignity. Still, as the finale for a successful first season, it's substandard.
Ironically, Invasion of the Body Snatchers was remade about ten years after The Original Series, with the new version featuring Leonard Nimoy.
Remastered: The new version is nothing too fancy, with new shots of the Enterprise, the planet, and the local star. Curiously, the creators of the original episode went all out with the visual effects for this one, spending a pretty penny on a new, more realistic planet and a star. (They should have saved the money for the live Oddly, despite being designed specifically for this episode, the colors of the planet sphere for the original footage don't exactly match the look of the live action scenes (which look like Earth, because they were shot outdoors, partly at an electronics labratory with some fancy architecture and partly at UCLA). The new version creates a more seamless transition between the effects and the live action footage by featuring a more Earth-like planet. (It also has the side benefit of better selling the idea, central to the plot, that there are millions of people living on it). The star is upgraded as well, appearing a little more solid. Perhaps most ambitiously, CBS Digital replaces a couple of redundant live action shots with CGI shots of a satellite, so that it's not just talked about but actually seen.