One of my favorite moments in the OT is when the three have just escaped from the garbage masher, and Leia starts complaining about Han... at the beginning, Han totally ignores her - specifically, here is a princess trying to get Han's attention and give him an order and he doesn't even acknowledge her, he's too busy barking at Chewie, calling him a coward. I really think that scene is masterfully done and shows the degree to which Han doesn't give a rat's a** about someone's rank.

I also like the scene when he and Luke are in the cockpit talking about Leia. Although Han expresses his interest, he seems to be doing it as much just to tease Luke.

By contrast, even in ESB Han's dialogue was a bit less carefully crafted. Although it had moments of brilliance ("I love you" - "I know").