The scene is important the first time you watch the movie, because at that point you've just met Han, in a scummy bar, and you aren't sure about him. Han coldly shooting Greedo nails down his character. Without it, he starts out a good guy and stays a good guy. Han coming back at the end to save the day isn't a transformation. Of course, once you've seen the movie it doesn't matter anymore.
As for the effects of blaster fire on Greedo; do we actually see anyone, besides Greedo and Stormtroopers, get shot? I don't recall if we actually see any of the officers in the detention level get hit, and the stormtrooper's armor would hide the damage. Beru and Owen were charred far worse than Greedo. It's possible that blaster fire causes severe burns, and Han's pistol is seriously overpowered.
More interesting is how Vader killed Obiwan without cutting his robe, or having his blade stopped by Obiwan's.