a volcano is definitely not a hollow mountain that contains swirling pools of lava and islands of solid rock. and if such a thing were possible would not the atmosphere within be at least as dense and ash laden as the stuff that is coming out the top. then spock throws in what is later referred to as a "cold fusion device". cold fusion if made feasible could only create massive amounts of energy which would only exacerbate the situation.
and what on earth were they thinking when not one but two technological advances were introduced which now give star fleet the ability to revive a dead person and the ability to transport instantaneously to anywhere in the universe? thanks to the writers infinite wisdom i will now be sitting and watching all subsequent sequels and saying "why on earth don't they get some of kahn's blood? why on earth didn't star fleet keep kahn in a coma and harvest his blood until every vessel is equipped with 20 pints?" similarly "why aren't they using scotties transwarp device to transport across the galaxy?"
and while we're on the subject of transwarp, is it just me or did it appear that the enterprise spent 5 to 10 minutes at warp speed before it dropped out of warp and was within shuttlecraft range of the klingon home world. and while on the klingon homeworld we only get to see one klingon. the rest of the klingons wore body armor. did the special effects budget cut into the prosthetic make up budget? answer: yes very likely.
carol marcus has a doctorate in applied physics yet she fails to realize the futility of running in a random direction in order to avoid beam up.
photon torpedos are people?
kirk uses 20 shots from a high powered phaser rifle in a failed attempt to break through the shields of kahn's blackhawk hovercraft. he then throws the phaser rifle at the hovercraft and it breaks through the shields and crashes the ship.
calling old spock was lame and pointless and it will afford situations in sequel films where viewers will ask themselves "why don't they just call old spock?"