Same can be said for Shatner, but people tend to ignore that one.
Shatner was, according to "Star Trek Lives," scheduled to direct the final episode of the Original Series in 1969. Unfortunately, that would have been Episode 81, and NBC sent the word down during the filming of "Turnabout Intruder" that that episode, #79, would be the last.
In his book I Am Spock, Nimoy mentions that DeForest Kelley kept swearing up and down in the scenes where McCoy converses with an unconscious Spock that Nimoy was trying to direct him through the movement and flutter of his eyelids.
Fake Russian: In letter, but not in spirit. Chekov actually speaks Russian for the first time. Though Walter Koenig was born in America, his parents are Russian immigrants who emigrated from Lithuania.
"Up your shaft" is not a nice thing to say to your Director, Scotty!note The Excelsior turbo lift was voiced by an uncredited Leonard Nimoy.
The Other Darrin: Kirstie Alley loved playing Saavik (she apparently wore the ears home a number of times) and wanted to return, but apparently failed to communicate this clearly to her agent, who demanded a higher fee for her to play Saavik than Paramount was willing to pay. Paramount switched in Robin Curtis instead.
Throw It In: Kirk stumbling off the chair after being told David was murdered was entirely accidental, but Leonard Nimoy felt it suited the scene, and left it in.
To be quite exact: Shatner stumbled on a previous take, whereupon the two convened and decided that the scene should include such a gesture. The recorded take was then staged, leading to the movie we now know.
Early scripts has the Klingons as a rogue group who commandeered a Romulan Bird of Prey.
And earlier than that, it was supposed to be Romulans, period, in Harve Bennett's treatment. Spock's role is relatively the same, except he goes feral and kills several Romulan miners when they drill for dilithium on the Genesis planet. A subplot would have also had the Vulcans threatening to secede from the Federation over the Genesis Torpedo...
In the novelization, Saavik and David Marcus became romantically involved (the seeds for this were planted in the previous movie's novelization); this storyline was completely dropped from the films.
In the novelization, Saavik became pregnant with Spock's kid. This, too, was dropped.