Problems with calculation
Act utilitariniams offers a clear and straightforward way of discovering what is right or wrong. However Mill considers this objection:
'It is not possible to calculate how much happiness an action will cause'
however this objection misrepresents what utilitarians say. Bentham does not say an action is right if it actually maximises happiness, he says it is right according to the "tendency it appears to have" to maximise happiness. Thus an action is right if we can reasonable expect that it will maximise happiness.
Happiness is still a complex concept to apply directly to actions, but Mill claims we dont need to, as over time people have decided what does and does not produce happiness, this is what inherited moral laws tell us, e.g dont steal, dont lie, keep your promises.
Mill calls these moral rules (dont steal, dont lie) secondary principles.
It is only in cases of conflict between secondary principles such as (lying to not break your promise) that we need to apply the greatest happiness principle to any action. We should not attempt to calculate happiness unless we have a conflict.
Our inherited morality still makes mistakes in what it thinks will or wont contribute to our general happiness, so we can improve on the rules that we have. But saying this is quite different from saying we must consider each action from scratch.