1) The basic principle of Mill's Utilitarianism is the greatest happiness principle (PU): an action is right insofar as it maximizes general utility, which Mill identifies with happiness.
NOTES:

• Each person's happiness counts as much as anyone else's; hence, Utilitarianism is not a form of ethical egoism in that it does not require me to pursue my own happiness.
• PU doesn't say that we should promote the "greatest good for the greatest number,"  although often that is the way to maximize the aggregate amount of happiness. Indeed, Bentham seems to have adopted the principle "greatest good for the greatest number."
• PU introduces a gradation of right and wrong actions.  However, the best action (the one we should engage in) is that which, among the available options, maximizes general utility.  Consequently:
1. If  act X produces much general utility, it doesn't follow that X the moral (i.e., the best) act.  There may be other available options which produce more general utility.
2. If act X produces general disutility, it doesn't follow that X not the moral act.  All the available options, including doing nothing, may be bad, and X may be the 'least bad', as it were.

1. pleasure and absence of pain
2. the only desirable end, the final good. Every other desirable thing is so either for the pleasure it provides or as a means to pleasure.

Objection: "Happiness is pleasure" is a doctrine worthy of swines.
Utilitarian reply:
3. Bentham: Pleasures are all qualitatively alike;  however, they can be graded on the basis of intensity, length, certainty, temporal closeness, fruitfulness and purity.  It turns out that higher pleasures are ultimately better and therefore should be preferred on the basis of UP.
4. Mill:
   • pleasures can be distinguished not only quantitatively, but qualitatively as well.
   • It turns out that those who are equally acquainted with both higher and lower pleasures prefer the former.
   • the best explanation of this preference is that humans have a sense of dignity in some proportion to their higher faculties, and that dignity is an essential component of happiness, so that any pleasure conflicting with it is rejected.

     
     Problems:
     What's the evidence that people well aquainted with both higher and lower pleasures prefer the former?
     Is the appeal to dignity in appropriate?  In particular, what's the evidence that a sense of dignity is an essential component of happiness? Does Mill run the risk of making the satisfaction of the sense of dignity a final good on a par with pleasure?

3)  The hedonistic calculus used to determine which course of action to take follows the pattern of cost-benefit analysis, which involving 5 basic steps:

1. Determine the alternative courses of action
2. Determine the consequences of each alternative
3. Assign value to the consequences and implementation costs of each alternative on the basis of how much happiness is destroyed/produced.
4. Calculate the net benefit (cost) for each alternative
5. Choose the alternative which optimizes net benefits

NOTE: Steps (1)-(2) are about facts, not values.

• Step (1): How does one know that all the feasible alternatives have been considered? 
• Step (2): Often (though not always) it's very hard to determine the consequences of an action or a  policy.

Reply:
We do what we can.  If the objection were good, then there would be no point in planning ahead or in distinguishing a wise man from a fool.
• Step (3): The good for Utilitarianism is happiness, i.e., pleasure.  But it is almost impossible to determine how much pleasure an action or a policy will produce.
• Often there's no time to perform any sort of calculation.

Reply:
Then we can use rules of thumb which a long experience has shown to be usually successful.  This is why even if a rule of thumb fails in a particular case, we don't automatically discard it.

PU tells us to maximize happiness.  But one can (perhaps surreptitiously) maximize total utility irrespective of distributive justice, need or merit e.g., by making few undeserving and already happy people fabulously happy at the expense of many rather unhappy, deserving people.  Conversely, PU might require radical, and many would say unjust, redistribution of property from the minority to the majority.
 
Reply: Society does not distribute happiness but goods (e.g., money) which generate happiness in people who have them.  But, the law of diminishing marginal utility tells us that goods produce more happiness in those who have few of them than in those who have many (if you give $ 1,000 to Bill Gates, he won't even notice; if you give them to me, I'll be ecstatic).  Hence, other things being equal, people in need should be satisfied before people with no need.  Similarly, since gaining desert involves disutility (e.g., work, stress etc.), other things being equal, deserving people are capable of greater marginal utility than non-deserving   ones, and hence should be satisfied before non-deserving ones.  Analogously, the need for stability and security in the planning of one's life would drastically limit any radical redistribution of property to the majority.
NOTE: these are, however, contingent reasons; nothing in utilitarianism is essentially against drastic redistribution of any sort.
 

PU tells us to maximize general happiness. But happiness might be maximized by trampling on somenone’s or some group's rights.  For example, enslaving a few might maximize happiness if the needs of the many are thus met. This is very bad because the moral obligations involving rights are especially stringent.
Reply:
For Utilitarianism, rights are parasitic on general utility.  So, for Mill one has a right only if society benefits from it.  However, this is sufficient to guarantee certain rights, e.g., to security (otherwise vigilantism), to free speech (society is better off with free market of ideas), property (more goods to go around) etc. So, Mill can claim that certain acts are not just wrong because they don't maximize utility, but unjust as well because they impinge on one's right. Still, how many rights PU can actually generate is unclear.

Utilitarianism seems to view people as vessels of pleasure and pain rather than as persons: as long as utility is transferred from one subject to the other without spillage, as it were, the utility level remains the same.  This seems to be the source of problems (A) and (B).
Reply: Impersonality guarantees impartiality, namely that each individual is treated the same when it comes to happiness.
Duplication: Impersonality is not a necessary condition for impartiality. Impartiality can be achieved otherwise, e.g., by analogues of Rawls’s original position.

Consequentialism claims that what we ought to do is solely determined by the value of consequences of what we do.  Although Utilitarianism is by far the most developed and popular version of consequentialism, it is by no means the only possible or reasonable one. In this context it may be helpful to distinguish among various types of consequentialism on the basis of which consequences of an action are deemed morally relevant.  For example, one might hold that only the consequences affecting the agent are morally relevant (perfect egoism), or that only those affecting others are relevant (perfect altruism), or that it makes no difference who is affected by the consequences.  But even if one restricts one's attention to the last type of consequentialism, there are still at least three reasonable options available: 

1. Hedonistic consequentialism, which identifies utility with pleasure and absence of pain (this is utilitarianism proper).
2. Subjectivist consequentialism, which identifies utility with the satisfaction of individual preference.

Problem: It collapses the desirable into the desired.  But the two at times don't coincide.  For example:
• people often don't know what's good for them or are unable to choose it because of lack of information, irrationality, false consciousness, or weakness of the will.
• one might argue that some things, e.g., love, beauty, friendship, are good, no matter whether they be desired or not.
3. Welfare consequentialism, which identifies utility with the satisfaction of interests rather than mere preferences.

Problem: it's hard to come up with a list of “true” (vs. merely perceived) interests.