Ben Stiller, admittedly
a big "Star Trek" fan, named his production company "Red Hour Films"
after this episode. Stiller also incorporated the Kirk vs. Spock
scene from "Amok Time" as a parody into his movie "The Cable Guy".
(see Behind the Scenes entry for
"Amok Time" also)
When Landru appears in the dungeon, one of the security guard actors misses his cue and covers his ears a couple of seconds before Landru starts his sonic bombardment and everyone else reacts.