Yes you would think a ship specifically searching for and examining planets would know one was missing. Or that the one they were scanning perhaps wasnt... say... the same size and type as the one that was supposed to be there? Or how about... something somewhere telling the captain "Beware, a madman called Khan is on the next planet over".
Also, you would think a genius would get the 'hours and days' thing. Of course you would have to accept that for some reason encrypted transmissions were not possible anyway. Or if they were, certainly all encryption codes would have been invalidated once it was known Reliant was in unfriendly hands. The 'only ship in the quadrant' thing is a tiny groaner also because the ship was near Earth anyways. At least I would assume so since AFAIK it never used warp drive until Kirk took over. So... that means there were no other starships at Earth?
Anyways... just stupid minor details that mean nothing but something to have a little fun with. I doubt I still have it but MAD Magazine did a ST2 spoof that was great. Same kind of stuff.
"Jim, I'm your doctor and I'm your friend. As your friend I say get back your command. As your doctor you owe me 50 bucks"