The obvious problem with this are that it is impossible to know all the outcomes of a certain dilemma. For example if we were to shoot Sadam Hussein because of the pain he causes other people, we can assume that if he is dead it will maximise happiness but not if by this action there is an uprising and World War III begins where far more people may be hurt. We can only guess what is probable to happen but cannot predict all the outcomes.
One of the appeals of Utilitarianism lies it's the practical value, that it can be applied quickly to any moral dilemma. This is done in a mathematical form, by computing pleasure in the Hedonic Calculus. This is Bentham's way of deciding on the correct or most appropriate course of action by analysing the pleasure that arises from it and comparing it with alternatives. He identified seven factors involved in this process, Intensity, Duration, Certainty, Propinquity, Purity, Fecundity, and Extent which help us weigh an asses the quantity of happiness. One of the problems with the Hedonic Calculus was that it judged the quantity of happiness i.e. the number of people but not the quality of the happiness therefore problems arise in assessing it's value. Different pleasures bring different amounts of happiness to different people but in Bentham's theory all pleasures are equal. This received much criticism from Victorian society as like Epicurius he commanded all to enjoy "swinish" pleasures which were frowned upon by the educated classes at this time.
Mill attempted to tackle this pitfall by acknowledging that there were higher and lower pleasures. His proof was based on human experience and proposed that no one who has experienced a higher pleasure would sacrifice that knowledge for an experience, however intense, of a lower pleasure. This is illustrated perfectly in the play "Educating Rita" by Willie .where a working class woman experiences the higher pleasures of literature and feels as if she no longer belongs in a pub experiencing lower pleasures.