Corrected entry: When the Enterprise first encounters the Reliant, we see several screen shots of the Reliant on the Enterprise viewscreen, and several shots of the Enterprise on Reliant's viewscreen. The puzzling thing is, if you watch very closely to the shots of the Enterprise on the Reliant's viewscreen, you will notice that the stars are actually moving BACKWARD, as if the Reliant were in a slow reverse. Obviously this is an editing blooper since Khan just ordered that the ship slow to one half impulse power, which still moves the ship forward.
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).
Garlonuss
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.
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.
Quantom X 
Correction: Trek canon has shown the viewscreens are not the same as windows, and that the screens can show us views from vantage points where no camera exists. These vantage points also do not need to be stationary. As such, the views of Enterprise on Reliant's screen are taking Enterprise's speed into account, and the 'vantage point' is backing up to keep her 'in the shot' while Reliant is still moving forward.
johnrosa