Now, since the subject of Star Trek II is suddenly thrust upon us, I have a fair few criticisms of that movie. Bear in mind, I grew up with Star Trek II and still think it's the best of the ST movies thus far produced. I was so obsessed with that movie as a kid that I learned the dialog verbatim. I can still quote it 30 years later. But anyhow, I digress.
First Criticism: The People In Charge Are To A Fault Small-Minded
Star Fleet is established as being a massive, multi-species, multi-system organization which is a part of the United Federation of Planets. For such a truly massive entity, they have so very very very few ships, and they're not well deployed. Realistically, Star Fleet ought to be portrayed as having tens- or even hundreds of thousands of ships. No, not all of them would be Constitution Class or Constitution-Refit Class, but without a doubt there should be a lot of those, too. To say that Enterprise "is the only ship in the quadrant" is completely idiotic. The writers obviously have no concept of what a "quadrant" actually is, or what the term clearly should imply.
Second Criticism: The Under-Realized Potential of Opportunism *and* Geography
In the run-up to what would have been Reliant's original mission, Star Fleet composed a list of potential candidate systems for the Genesis Phase 3 test, one of which included the Ceti Alpha system. In any organization of the type and nature of Star Fleet (for example, the U.S. Navy, or the British Royal Navy, etc.) activities of any significance get seen by, and often probably have to be approved by, security and/or intelligence-related departments. If we go based solely on what's shown in the movie and what's in the accompanying novel, Khan's re-discovery 15 years earlier and his sentence to Ceti Alpha V are not public knowledge. Likely, they are classified. That means, when the Ceti Alpha system would have been floated as a candidate for the Genesis test, one of two things should have happened. Either it should have been pulled from the list with some or possibly no reason given (in which case Reliant would never have gone there) or someone with a devious bent of mind should have green-lighted it, knowing full well that likely the test would have had the potential of wiping out other occupants in the system. After all, if Genesis was super safe, why not trial it in the Sol or Eridani or Betazed (etc., etc.) systems?
Third Criticism: Just How Incompetent Are We To Believe Reliant's Crew Is?
There were star charts of that system. Moreover, it would take a heck of a lot more than one planet exploding to cause Ceti Alpha V to change its orbit *at all*, much less to a significant degree. Moreover, planets don't just explode. That's not a thing. And if somehow CA VI *did* explode, dedicated science vessel U.S.S. Reliant wouldn't have detected anything? Again, we're talking (per Khan's account) 14 years and six months ago. That's not a lot of time for planetary-scale debris to travel. And nobody ever thought to ask "Hey, where's planet six of this system?"? Really? Sorry, but I don't buy it.
Fourth Criticism: Why Don't Ships Have Their Shields Up All The Time?
This is really not a criticism of ST:II so much as it is a criticism of the franchise as a whole. There's a LOT of crap floating around in "empty" space. Everything from stray subatomic particles to asteroids hurtles through space at speeds of at least 15,000 - 30,000 miles per hour. Many things travel significantly faster than that. Beyond that, when you're traveling using warp drive, you're potentially making the situation much worse. There's videos on YouTube which model what happens when you slam something into Earth at near the speed of light. And at super-high velocities, the tiniest of things can cause well beyond catastrophic harm. TL;DR: If you have shields, you d**n-well use them.