"Khan doesn't see through Spock's silly code". Who says he doesn't? His actions wouldn't be influenced by this one way or another - indeed, he seems positively delighted when the Enterprise
is "not so crippled after all", and might well have been anticipating the revelation.
"Planet can't become lifeless so quickly". Nonsense - all life could be lost in mere seconds in suitable circumstances. But we need not assume that. Our heroes thought there was nothing but us lichen down there when there were dozens of live humans inhabiting the surface - so it was a matter of sensor performance, and the cataclysm that nearly killed Khan's colony had made the planet impermeable to the usual sensors. There might have been life aplenty, our sidekicks were just unable to see it.
"Ceti Alpha" must be "Alpha Ceti". Further nonsense, especially in view of the TOS and general Trek habit of using extremely truncated star names. We have places called "Omega" or "Alpha", indicating that omission of "generally known data" such as the constellation being discussed is common in Starfleet. It would only be in keeping with Trek tradition that Epsilon Ceti A would be truncated to Ceti A(lpha), while Omega Eridani B might become Omega Bravo or the fourth planet of 334 Reticuli could become planet 334-IV.
As for membership in a certain constellation placing limitations on where a planet must be... Well, hardly. Constellations may span huge swaths of the celestial sphere, and cover basically an infinite range of distances. Cetus certainly caters for real targets near and far, but Trek offers a range of potential "new" targets as well - stars hidden behind (real or fictional) dust clouds or space anomalies when viewed from Earth but visible when viewed from Vulcan, and falling nicely within an established Earth constellation.
"Inhabited worlds around unsuitable stars". Yup, common scifi mistake - but Trek has the perfect excuse. Some 99% of inhabitable planets in that universe would by all rights be the result of terraforming anyway (humanlike creatures have been at it for billions
of years!), and there are several cultures quoted with the ability to construct planets from scratch.
"Starfleet doesn't know about Ceti Alpha events". Well, it shouldn't - there's no evidence of a realtime scanning mechanism across distances greater than a couple of lightyears. And the "lightspeed shadows" of distant past events are so conspicuously absent from all Trek that we might just as well postulate a damping medium - one also responsible for hiding the radiation signatures of civilizations and spacecraft from 20th-21st century Earth observers. Heck, perhaps this medium also damps the color of stars and nebulae as it passes into our star system, so that they shine so brightly in close (starship) view in contrast to what they really look like as viewed from Earth... And is responsible for occasionally making it necessary to slow down to impulse when approaching Earth. We're the London of the future, with the infamous subspace smog problem!
doesn't establish facts diligently enough". Why should she? It's not as if Kirk ever bothered to do surveys of entire star systems when homing in on a specific planet, either. Star systems really are a dime in a dozen, and the Reliant
crew is bored out of their skulls already in this stupid hunt for these strange Goldilocks deserts that apparently have to be life-compatible but still lifeless. Anything but a quick in-and-out would be contrary to their mission goals, and any wasted time might well mean horrible death of a distressed colony or a successful Klingon raid somewhere down the line.