I agree that you dont have to be a prefect in order to be HB or HG. I think Dumbledore primarily chooses them by their maturity, smarts, and leadership abilities. Now, we all know that James's maturity level may not have been up to par, but maybe during the later years of his Hogwarts life he became more mature (in order to win Lily's heart) =]
He was obviously smart, as he was VERY good at transfiguration, and just spells in general since he was a key maker in the Maurauder's Map. I think he was a good choice for HB, even though he wasn't a prefect.
(Oh, and I think that Dumbledore just wanted to help Lily and James's relationship:] )