Corrected entry: Kahn explains that Ceti Alpha VI exploded and altered the orbit of the Ceti Alpha V, laying everything waste on the planet. Okay, fine. How then did they mistake Ceti Alpha V for Ceti Alpha VI? Star Trek has established that their method for numbering planets is based on orbit position numbering outward from the star at the center of the system (Earth would be Sol III if it didn't already have other names). For Ceti Alpha V to be mistaken for Ceti Alpha VI, there would have to be another planet inserted between Ceti Alpha V and the star (Ceti Alpha). There is no way for an explosion at Ceti Alpha VI to send a new planet in past Ceti Alpha V and the only way for the explosion to push Ceti Alpha V away from the star would be if the planet had exploded while on the other side of its orbit from Ceti Alpha V. If that had happened, the shockwave would not have been nearly enough to sent Ceti Alpha V up two orbits (because Ceti Alpha VI is gone so Ceti Alpha V would have to go up past Ceti Alpha VII).
Corrected entry: Doesn't it strain credulity that the Enterprise is (once again) "the only ship in the quadrant"? In Star Trek terminology (all series), a quadrant covers one fourth of the galaxy (smaller regions are "sectors" and the boundary runs just about right down the middle of the Federation, right by Earth to be exact. Are we to believe that there is no other starship in that entire half of the Federation?
Correction: Before ST:TNG, "quadrant" was a term used somewhat loosely. In the Wrath of Khan, quadrant does not refer to one quarter of the galaxy.
Look up the term "quadrant." In every single applicable variation it is some form of "one quarter of a circle."
According to memory alpha, the star trek wiki, a quadrant is a major region of space encompassing a portion of a galaxy. There are apparently major and minor quadrants. The major quadrants are the 4 quadrants dividing up the milky way. Minor quadrants of course encompass a smaller part of said major quadrants. How large is seemingly quite inconsistent though. I think it has been settled upon that a minor quadrant is a couple of sectors (4) large.
Sulu also mentions that Reliant (which is in visual range, approaching at half impulse power) is in the same quadrant, which going by the post-1987 definition would be like saying the car approaching down the street is on the same continent. It's pretty clear that when they mention a "quadrant" in this movie, they are not referring to a quarter of the entire galaxy.
Corrected entry: When Enterprise finally defeats Khan in the Motara Nebula, Uhuru starts transmitting the order to surrender for one minute and 18 seconds before Khan activates Genesis. That was more than enough time for the Enterprise crew to beam Khan on board the enterprise and either arrest or kill him. (01:28:48 - 01:30:06)
Correction: The nebula interferes with a lot of systems. The sensors were not functioning and they could barely get a clear visual on the viewscreen. The transporters would not be able to lock onto Khan.
Correction: But they were still inside said Nebula. You saw how it was interfering with their shields, communications and the likes. Just imagine what could go wrong if you tried beaming people around in there.
Correction: The explanation here is pretty simple. Ceti Alpha V must have been where Ceti Alpha VI was supposed to be. With that said, the captain and crew could have easily assumed that Ceti Alpha V was Ceti Alpha VI and that Ceti Alpha V must be on the other side of the system, hiding behind the star. Obviously, the system isn't visited often. Otherwise, Kirk wouldn't have picked the Ceti system for Khan 15 years earlier. So, it's easy for the captain and crew of the Reliant not to be aware of the explosion of Ceti Alpha VI and the shifting of the orbit of Ceti Alpha V. With minimal information about the system (other than the fact that Khan was on Ceti Alpha V), they could have easily mistook one planet for another, especially if they have similar characteristics. The fact that Chekov thinks they're on Ceti Alpha VI when they beam down confirms this. Also, the fact that Khan says that Kirk (and no one else) bothered to check on their progress in 15 years confirms that the system is not visited often. So, what seems like a plot hole can be easily explained.