Okay, so when Chekov and Captain Terrell beam down to investigate the planet for suitability for the Genesis Project, they think the planet is Ceti Alpha VI. Then, when Khan explains that
THIS IS CETI ALPHA FIVE, he says that Ceti Alpha VI asploded—secretly!—fourteen-and-a-half years ago. This is stated as the reason why Ceti Alpha V looks a lot less hospitable than it did during TOS, and it's presumably the reason why the crew of the Reliant weren't capable of accurately counting to six.
Planetary systems are numbered from the inside out. Ceti Alpha Prime would be the planet nearest the star, Ceti Alpha II would be the next one out, then Ceti Alpha III, IV, and Ceti Alpha V would be inside the orbit of Ceti Alpha VI. So when the Reliant warps in on its planetary survey mission, they count planets Ceti Alpha one two three four five six... and beam down to the wrong one.
If Ceti Alpha IV had asploded, they might be forgiven for getting the name of Ceti Alpha V wrong. There would still be the pressing issue of a suspicious-looking additional asteroid belt that wasn't on the charts. But when Ceti Alpha VI asploded, six months after we were left here, the only planets that change their name are Ceti Alphas VII and onwards. The only way for Chekov and Terrell to end up on Ceti Alpha V in a system that, unknown to them, has the sixth planet missing, is if they were actually trying to beam down to Ceti Alpha VII and they still fucked that up.
This has bugged me for thirty years, and no amount of Ricardo Montalban's acting can change basic planetary physics. No, Ricardo, stop trying to distract me with your chest. This isn't even basic planetary physics, it's basic planetary arithmetic.
Also, did the star chart not have a big X marked on it, with
Here be incredibly dangerous genetically engineered criminals from the 20th century? Did Kirk not actually tell anyone when he established a colony of psychopaths in a habitable system at the end of `Space Seed'? Carol Marcus does mention, only fifteen years afterwards, the galactic problems of population and food supply. Did Kirk hide a bunch of incredibly powerful, genetically-engineered lunatics on a valuable planet, and then try to act surprised when an innocent survey vessel caught hell for it later?
I used to own The Nitpicker's Guide to Star Trek (unsurprisingly), and it went on at length about Kirk apparently forgetting to notify Starfleet about the nest of big-titted maniacs he left carelessly strewn about the galaxy. It didn't mention that Ceti Alpha V cannot be mistaken for Ceti Alpha VI. The guy who wrote the Nitpicker's Guide also failed to count accurately to six. This bugs the hell out of me.