Continuity mistake: When David and Saavik approach Spock's tube on Genesis, you can see quite a bit of dirt covering the words' red lettering, but when it does another shot of the lettering, it is noticeably cleaner. (00:30:25)
Continuity mistake: In the scene early in the movie where Kirk is talking to Sarek the guns on the wall are suddenly rearranged. (00:23:50 - 00:24:45)
Revealing mistake: When the Enterprise explodes, some of the debris briefly turns transparent. (01:12:15)
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.