.The question of how they could have missed a planet exploding not to mention that they could simply count the planets around the star in TWOK is a tough one.
I tried to rationalize this in a novel by suggesting that, entering the solar system from the outside, and counting backwards from the outer edge of the solar system, one could easily assume that Alpha Ceti V was Alpha Ceti VI if you had absolutely no reason to suspect that an entire planet had gone missing. Especially since, in real life, solar systems are huge and the planets aren't neatly lined up in a row the way they are in textbooks.
(Granted, this assumes that nobody used any long-range scanners to count the number of planets in the solar system, but why would they? Planets don't routinely disappear.)
As for nobody noticing that a planet exploded . . . well, space is big and this system was supposed to be way off the beaten track, which is why they were thinking of testing the super-secret Genesis Device there in the first place. It was a remote, largely unexplored system that nobody had visited for decades, so the planet's explosion went unnoticed.
It's not like Vulcan blew up or something.![]()
This is something I always wondered personally: why do fans seem to assume Kirk mentioned stranding Khan to Starfleet?
The guy is a genocidal mass murderer, responsible for untold war crimes and destruction. If you told the world governments that you'd found Adolf Hitler in space, but given him his own planet, it seems unlikely they'd shrug their shoulders and go "your call."
I always assumed that Starfleet didn't know about Khan. That would explain why they'd be so reckless as to test the device next door, and maybe even why they wouldn't feel the need to count the planets when entering the system. After all, it's not that big a screw-up when you take the genocidal madman out of the equation. "Hn, wrong planet. Move along, nothing to see here."
Given the themes of the film, I've always figured Kirk never told anybody off his ship about Khan due to his own arrogance and hubris. And so everything comes home to roost.
(Then again, I like the script's implication that Kirk never knew about David more than the "you told me to stay away" logic the film handwaves.)