The second season rarely featured Lt. Sulu (George Takei) and Ensign Chekov (Walter Koenig) in the same episode. Koenig was, in fact, cast as Chekov to fill in for Sulu in the first few episodes of the second season, while Takei was still involved in the filming of The Green Berets (1968). The two characters usually alternated between episodes. The episode "Amok Time" is one of the few second-season examples of their appearances on-screen together.
Celia Lovsky (T'Pau) was unable to make the Vulcan salute by herself. The filming crew taped her fingers together in the appropriate groups, and placed her hand flat on the armrest of her chair in the configuration. She then simply raised her hand into view, already in the salute.
According to Leonard Nimoy, Celia Lovsky couldn't actually do the Vulcan salute naturally, so she had to use her other hand to put her fingers in the right pattern below camera, then hold it up at the right moment.
Season 2 introduced new opening credits. DeForest Kelley's name was added to the "starring" cast and the theme music was extended and had the female soprano voice Loulie Jean Norman and percussion added to it.
"Amok Time" was the first aired episode in Season 2, but according to DVD Commentary, was actually filmed fifth. Star Trek: Catspaw (1967) was the first to be filmed for the second season but would not air until over a month after "Amok Time" as the seventh episode of the season.
The prequel series Star Trek: Enterprise (2001) considered having its regular Vulcan character (played by Jolene Blalock) be a younger version of T'Pau. Since that would have required paying a fee to the estate of Theodore Sturgeon the author of Amok Time, this plan was abandoned and the new character was rechristened T'Pol. T'Pau did feature as a guest character in a few episodes of Enterprise's fourth season.
In the original script, there were a few more Vulcan words. Spock described Kirk and McCoy as his lak noy, the equivalent of best man. When T'Pring makes her challenge, the wedding party begins to discuss what's going on, all in Vulcan, until T'Pau shuts them up.
At the onset of the Koon-ut-kal-if-fee, T'Pau is clearly seen initiating a prolonged Vulcan mind meld. T'Pau begins the meld by carefully positioning her fingers on his face as Spock kneels before her. Kirk and McCoy are shown as they observe from several feet away. The camera returns to show T'Pau continuing to meld with Spock. We then see Stonn and T'Pring observing from their viewpoint. As the camera returns to T'Pau, Spock rises from the meld and withdraws. T'Pau appears to have been assessing Spock's readiness to commence the ceremony. Her later statement that Spock was deep in the plak-tow (blood fever) stage may have been confirmed by the mind meld. A similar ceremonial mind meld can be seen at his Kolinahr ritual in Star Trek: The Motion Picture (1979).
The trivia item below may give away important plot points.
One of only two times in Star Trek (1966) where Spock shows an emotional reaction without being influenced by something - if only for a few seconds. The other example is the primitive pilot Star Trek: The Cage (1986), filmed when the rules hadn't been established for this character.