The populace of Missouri just voted to ban gay marriage. This illustrates one of the disadvantages of direct democracy -- it's worse at preserving minority rights.
Suppose a minority is seriously harmed by some proposal, while the majority is unaffected and supports it. If you're a representative, it's often smart to vote against the proposal. Sure, you go against what most of the people think, but most of the people will forgive you. You can still win their votes on other grounds. The minority, however, will get mobilized and organized against you. No matter what stances you take on other things, you've lost their vote.
Direct democracy is different. A bunch of people with vague feelings of unease about gay people getting married -- people like my dad, for whom this would never be a make-or-break issue -- can swing the vote dramatically.
Now, my guess is that the amendment would have easily passed a representative body as well. But I'd be surprised if it got 72% of the vote there.