Cool. I don't recognize it, but there might be experts here who have the movie or show down pat.
When the Reliant was dispatched to the Ceti Alpha system, why wouldn't Chekov think "Oh yeah, that's where we dumped Khan!"
Two equally likely explanations:
1) Because he wasn't told? If he wasn't the navigator on duty when Kirk ordered the ship to this place, he probably wouldn't have been given the memo. Kirk, Spock, McCoy and Scotty marooned Khan in a secret location because they didn't want to give him over to authorities - they liked the guy too much. They wouldn't have squealed to Starfleet, and they wouldn't have told their crew the specs, either.
2) Because he forgot? Chekov must have visited hundreds of star systems, the rate he was going in TOS. If Kirk had made sure there was no official entry about the marooning in the records, then browsing through the databanks for "Ceti Alpha: The Highlights" would not ring any bells for Chekov.
Also, the great, mighty StarFleet was completely unaware that a planet in this system exploded?
That is more or less the basic premise of Star Trek.
In that show, the only way to find out in real time what is really happening in a distant star system is to go and have a look. Telescopes don't reveal anything much, not in real time: the numerous star systems devastated by the Doomsday Machine were only revealed to have been reduced to rubble when Kirk's ship sailed into that rubble, again and again and again, system after system.
And you don't go and have a look lightly. Deneva, a system inhabited by "almost a million" people and a former major freight port, went silent and remained silent for "over a year" before Starfleet paid attention.
Kirk would have made sure that he dropped Khan in a location that would be even less frequently visited!
Carolyn Marcus wanted a planet that "was completely dead or the deal's off." Maybe next time send a ship with better scanners?
We've seen fancy ores and heavy weather screw up sensor readings before; that's probably the state of the art for Starfleet.
Oh...and now that I remember, once Chekov figured out where he was, why not call for an immediate beamout instead of going outside to be captured by Khan?
Because Chekov was scared out of his wits.
Which brings up another point, if they knew the scanners weren't reliable because of the storm, how can they be trusted to find a planet "completely lifeless?"
Very good point. Marcus' specs for the planet seemed extremely specific in any case, otherwise the Reliant
would not have spent such a long time looking. Not only would the planet have to be dead, it would apparently still have to be Class M (with breathable air, as seen).
Remember that the Marcuses wanted to solve problems of interstellar famine. Perhaps their main goal was to get crops growing on a dead and worthless planet - so their main concern would be finding a planet free of global plant life, and never mind isolated pockets of whatever. If Terrell could prove the desert world only had this one "Garden of Ceti Alpha", then the experiment could still proceed, despite lower levels of plant or animal life elsewhere.
The other possibility is that Marcus shied away from experimenting on a living planet for ethical reasons. The Genesis effect would still obviously work, and the experiment might even yield the desired scientific results, but some lichen would die and that would be a big boo-boo. But there could be limits to the practical application of high morals, and Marcus would be ready to give the go if the sensors showed nothing, regardless of whether there was invisible life down below.