The voices of the little creatures in the final scene are the sounds made by newly-hatched alligators calling for their mother.
A detailed metal prop miniature of the Enterprise was created for this episode, then laminated in lucite as one of Korob's tricks. The miniature was donated to the Smithsonian National Air and Space Museum by Gene Roddenberry.
First appearance of Pavel Chekov, though not the first one broadcast. That honor goes to Amok Time (1967). Notice that Walter Koenig was still growing his hair out and therefore had to wear a rather unconvincing wig.
The title of this episode, "Catspaw", is a term that describes a person used by another as a dupe. As McCoy points out, Scott and Sulu are used as catspaws to lure more crewmen down.
This is the first episode to feature all 7 of the "classic" cast members who would be brought back for future big screen adventures: Kirk, Spock, McCoy, Scotty, Uhura, Sulu, and Chekov, although they do not all appear in the same scene together.