I’m sure this isn’t the only bad science, and bad science doesn’t necessarily mean a bad movie, but I had to get this off my chest;
The Co-ordinates that Khan gives to Kirk lead Scotty to Jupiter. Here’s the problem - co-ordinates refer to a fixed point in space. The Federation is not an intergalactic organisation, so these co-ordinates must use EITHER the centre of the galaxy as a reference point, or possible the solar system (they are an interstellar organisation after all, so must organise based on Stars, not planets). Now, it takes Jupiter a hella long time to orbit the sun (over a hundred years, right?) and moves very fast - it covers an extraordinary area. My issue is this - how could Federation coordinates possible track a moving Jupiter? Jupiter - in the scheme of things - is ridiculously tiny.
Admittedly, Khan could calculate for Jupiter’s changing location within our solar system (itself moving around our stellar neighbourhood, itself moving around the galaxy) - its only maths after all - but he could only do that if he knew precisely when Kirk was going to visit… Which he didn’t.
WHY THE CO-ORDINATES!?!?
Also, The Enterprise warps away from Quo’nos (not Kronos) and is eventually shot out of Warp by The Vengeance. They end up about a quarter million kilometres from Earth. That’s within the orbit of the Moon! They went from an alien world to almost earth in a matter of minutes? How close is Quo’nos?! Lets look at the (very basic) Maths. The nearest star to ours is Proxima Centauri, in the Alpha Centauri System. Four light years away. It takes light (a starships speed at Warp One) four years to get there. Quo’nos is significantly farther than our nearest star - otherwise, they’d be in Federation space right? So then it would take tens, hundreds, thousands of years, more, for light to get from there to here. The Enterprise makes it in a few minutes (okay, so they’re travelling from the Neutral zone and not Quo’nos but the point still remains). This means they’re going significantly faster than the speed of light. Hundreds of thousands of times faster. More?
Light takes about nine minutes to get from the Sun to Earth - about four seconds to get from the Moon to Earth. If they’re going thousands of times the speed of light, divide that four seconds by respective thousands. If they had been shot out of warp a THOUSANDTH OF A SECOND LATER they would have overshot the Earth. Sulu wasn’t even reaching for the ‘throttle’ of the Enterprise!!! Imagine the quickest he could reach up and pull back was two seconds - they’d have overshot the solar system completely!
WHAT IS GOING ON? WHY THE SPEED?! It makes more sense in Spaceballs when the go to Ludicrous Speed!
Finally, Kirk dies for, like, minutes without being frozen (not even sure cryogenics would preserve brain function). Even magic Tribble Saving Khan Blood - IF it could bring back the dead (is Khan immortal?) - could not restore a brains function, especially if memory and consciousness are electrical impulses as they are theorized to be. Kirk would be brought back as a vegetable or a giant newborn baby.
WHY THE JESUS?