When Uhura is attempting to communicate with an alien using harmony, Ethan Peck (Spock) is unable to match her pitch. He is actually pretty tone deaf. Fortunately, the alien doesn't seem to care.
When Sam Kirk is stunned by a booby trap, the pose of him lying unconscious resembles his brief original appearance in Operation -- Annihilate! (1967), where William Shatner played him as a corpse for his brother Jim (also Shatner) to find.