Oh, I think TWOK has plenty of plot holes, contrivances, and internal inconsistencies that have nothing to do with continuity with TOS. How could the Reliant crew be unable to tell the fifth and sixth planets of a system apart or be unaware that a planet had exploded? Why wasn't there anything in the Starfleet databases telling them, "Hey, the Ceti Alpha system has dangerous genetically enhanced colonists so you should stay away from it?" If Chekov was on board during "Space Seed" as the movie claimed, why didn't he remember that Ceti Alpha was where Khan's people had been settled? Why was genetic supergenius Khan unable to pierce the screamingly obvious "hours could seem like days" code (which was even helped along by Spock pointedly stressing the word "hours" every time he said it)? Why would a security password that grants total access to a starship's computer systems be a measly 5-digit number? Why did Spock have to come all the way down from the bridge to sacrifice himself in order to save the ship when there was a whole engine room full of personnel with radiation suits? How could Kirk not even notice his second-in-command, most trusted advisor, and best friend had left the bridge without permission?
Of course, we could expand this right back to Space Seed. Why did the writers place the Eugenics War a mere 30 years in the future, which would imply that the genetic supermen were already being born when the episode aired? Why does the Enterprise need a historian, and why wasn't she or her successor consulted in any of the time travel episodes?
But they are the two most popular Trek movies ever made, despite their problems. So they both must've done something right, however much they both got wrong.
Technically, isn't IV more popular than II, at least based upon box-office receipts?