Other mistake: When Savic is sleeping, a burst of energy from planet pushes the tree she is leaning on upward. There is a Klingon above that almost gets hit with it. Savic should have seen him and started moving with Spock. This might have been a scene meant to be used later at the climax. (00:57:00)

Star Trek III: The Search for Spock (1984)
1 other mistake - chronological order
Directed by: Leonard Nimoy
Starring: Christopher Lloyd, William Shatner, George Takei, Leonard Nimoy, Walter Koenig, DeForest Kelley, James Doohan, Nichelle Nichols
Visible crew/equipment: When the Enterprise is exploding, a Klingon is shown flying over the helm. When he lands, a person's arm can be seen on the right side of the screen, trying to grab his foot. (01:14:50)
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Trivia: On the backside of the DVD near the bottom is a series of six images purportedly from the movie. The second image shows the crew in uniform, including Mr. Spock, standing in the Federation Council chamber. This image comes from the movie Star Trek IV: The Voyage Home (after the crew has returned to Earth and is waiting to hear the Council's judgment).
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Chosen answer: Kruge only had the proposal video that talked about what Genesis was. He didn't have any actual data on how Genesis works or how it could be created. Having footage of a nuclear blast doesn't give you knowledge about how to build a nuclear device.