Han was a cowboy. He dealed smuggling drugs (Star Wars calls it "spices") and other illegal paraphanalia. He lived in a rough and tumble world where he would be shot dead if someone was given the chance. He knew that and blasted away Greedo. It is of no consequence to him. Better safe than sorry.
And like you said, if anything was done in cold blood, he redeemed himself during ESB. Lucas is just an idiot. We know his films better than he does.