Continuity mistake: When Captain Kirk and the shape shifter are fighting on the planet (the shape shifter looks exactly like Kirk). They are rolling through the snow about to roll over Bones. In one shot, it looks like they will roll over his feet first, and then the rest of his body. In the next shot, it is a little closer and they roll over Bones' right arm first and not his feet first.
Continuity mistake: At the beginning, the USS Excelsior detects an approaching shockwave. One of the bridge officers is standing next to Sulu, delivering a report. When the camera angle changes, the same officer is seated at a console behind two standing crewmen. When the camera cuts again, he's between Sulu and that console, then sits to operate it.
Trivia: The Klingon who defends Kirk and McCoy at the trial is Michael Dorn, the actor who plays Worf in The Next Generation. The Klingon makeup is also identical, even though it is supposed to be a different character. (The makeup is actually more subdued than the makeup for TNG [flatter] but it looks similar because he is actually playing one of Lieutenant Worf's ancestors.)
Trivia: General Chang's line,"don't wait for the translation,answer me now" during the Trial is the same line used by American Ambassador Adlai Stevenson towards Russian Ambassador Valerian Zorin at the United Nations during the 1962 Cuban Missile Crisis.
Question: I don't understand why Spock insists that the magnetic boots must be on the Enterprise and not on the cloaked bird of prey. Spock points out that someone involved in the assassination conspiracy must be on the Enterprise, because this person must have altered the data banks. I agree with him. But why does that prove that the assassins who boarded the Klingon ship must have beamed from and returned to the Enterprise? How can he assume that the assassins and the computer hacker are the same person/people? Maybe there are assassins on the cloaked bird of prey and only a hacker on the Enterprise. Or, maybe the assassins might have beamed from the Enterprise but then carried on to the bird of prey, once their work was done, instead of returning to the Enterprise. And finally, if Spock does think the assassins beamed to and from the Enterprise, why is no one looking at transporter logs/records for evidence of unauthorized beaming to Kronos 1?