Greedo shooting first
Han's a bad-ass smuggler. Greedo is a bounty-hunter, where bad-assery is more or less a prerequisite. At that range, if either of them pulls the trigger, the other guy is going down.
It's a tense negotiation, with Han being held at gunpoint. Finally, with the gun pointing straight at Han, Greedo fires and takes half the plaster off the wall. What the fuck? Did he bend his blaster or something? He's supposed to be a bad-ass, but he can't shoot an adult human at a range of about 4 feet! That's so ham-fisted, he could make a knuckle sandwich sound quite appealing.
That's the bit that makes no sense. If there was a scuffle, lurching to feet, table thrown over, and *then* Greedo missed, it would be understandable. But to change history to make a shady character look like a nice guy is just stupid. You might as well have had Joseph Stalin in the editing suite...
Han's a bastard. He shot first to make sure he didn't shoot last. He's a smuggler, not a nice guy. That's who he's supposed to be. Put it back.