Our moral intuitions in fact do a very good job of arbitrating and coordinating human action given the unpredictability of the real world and the complexity of the game-theoretic issues involved, which utilitarianism is usually incapable of handling. (This is one of the main reasons why attempting explicit utilitarian calculations about real-life problems is one of the surest ways to divorce one's thinking from reality.)
If you have many convincing examples of this, you should write a post and sway a lot of people from utilitarianism.
This isn't the exact thing Vladimir_M was talking about, but: An Impossibility Theorem for Welfarist Axiologies seems rather worrying for utilitarianism in particular, though you could argue that no ethical system fully escapes its conclusions.
In brief, the paper argues that if we choose for an ethical system the following three reasonable-sounding premises:
Joshua Greene manages to squeeze his ideas about 'point and shoot morality vs. manual mode morality' into just 10 minutes. For those unfamiliar, his work is a neuroscientific approach to recommending that we shut up and multiply.
Greene's 10-minute video lecture.