Stupidity: When Sulu and the others were freezing on the planet's surface, a transporter malfunction interfered with their rescue. Kirk, Spock, etc., did not consider using the Enterprise's shuttle which could have flown to the planet's surface and rescued Sulu and the away crew.
Stupidity: In sick bay, Khan wants to read the Enterprise's technical manuals, explaining to Kirk he was once an engineer. Kirk acquiesces, saying they are available to ANY patient on the viewing screen. Apparently Captain Kirk does not seem to mind total strangers (this time with Napoleonic complexes) reading detailed documents outlining the strengths and weaknesses of a Federation starship.