Plot hole: There are 30-40 supermen, a big metal cargo container and who knows how many eel-things on the planet. How come only one of Reliant's scanners picked up a slight reading? I doubt it's the sand storm as A. they were able to get enough of a reading to beam down, and B. Enterprise was able to lock onto Kirk and co. through quite a bit of solid rock to beam them out of the Genesis underground test site even though she had heavy damage. Reliant has the same sensors as Enterprise and was in perfect shape, so why the lousy readings? Further, Reliant was scanning each planet for life down to the microbe level. So why can her sensors pick up microbes, but not humans and big metal boxes?

Continuity: In the scene when Khan first opens fire on the Enterprise, the exterior shots show the damage on the forward part of the engineering hull. However, the damage on the interior shots is occurring on the aft section. Which is to say if the exterior and interior damage lined up the way they're supposed to, Scotty and his cadet engineers would've all been killed in a warp core breach.

Continuity: In the Genesis cave, Kirk puts on his glasses to look at his watch. In the very next shot, he is not wearing his glasses.

Revealing: RE: The shot where Kahn's insect 'pets' are exiting Chekov's ear. The 'ear' could not possibly look more fake.