I've been a huge Star Wars fan since 1977. I love the original trilogy, and there is a lot to like about the prequels, even with the obvious flaws. When the special editions were released, there were exactly two changes I didn't like. Greedo shooting first, and Luke's scream. Luke's scream was BY FAR a much worse change, however, because it completely destroyed the momentous event of Luke choosing death over joining with his father. It was an alteration that changed the story significantly -- it meant that Luke was all bluster and no REAL conviction.
On the DVD's, Han and Greedo fire almost simultaneously, and Han is digitally shifted over the side. It's an unnatural movement. But, it is still better than the SE version. But my problem with the scene in either the SE or DVD version isn't so much an issue of Han's character, rather it is with how poorly the scenes were altered. Both versions just look unnatural. But who shoots first, to me, doesn't impact Han's character significantly enough to ruin the movie for me. It's a minor flaw, not a show-stopper.
But, beyond all that, they are still JUST MOVIES. Getting all worked up over them is a waste of time -- just enjoy them for what they are, or ignore them.