Recently, in the final game of World Cup, French midfielder Zinedine Zidane headbutted Italian defender Marco Materazzi for insulting him. In the aftermath, Zidane apologized in an interview with a French television but added that he didn't regret hic actions. Can one coherently apologize for an action yet not regret that action? Or is Zidane false in one of his claims (the apology or the lack of regret)?

That depends on exactly what he was apologizing for, and what he meant when he said he didn't regret the action. I'm sure that he was genuinely sorry that his action caused embarrassment and shame to France. That is quite consistent with believing that he was justified in his action, and that he would do it again in similar circumstances. That is probably what he meant by saying that he didn't regret the action. Of course, he might just have been inconsistent. There was an enormous amount of pressure on him to apologize. I suspect that most public apologies are insincere.

If a mother gives birth to a person who goes on to become a serial killer, has she done something immoral? Wouldn't a Utilitarian say that the act of giving birth to that child will decrease the general level of happiness? Great site by the way.

There are different versions of Utilitarianism. Some judge actions by their actual consequences, others by their foreseeable, or expected consequences. All judge actions in comparison with alternative possible actions. I doubt that the act of giving birth had any possible alternatives. However, you could just as easily ask your question about the act of conception, or rather the sex that led to the conception. Utilitarians who judge actions by their foreseeable consequences would not judge the conception of a serial killer to have been wrong, unless it could somehow have been foreseen that the resultant person would be a serial killer. Utilitarians who judge actions by their actual consequences might well say that the conception was wrong, but they would add that it was not blameworthy. Utilitarians, and consequentialists generally, distinguish between the morality of an action and the character of an agent. It is perfectly possible for a good or right action to reflect badly on the agent, or for a bad...