Utilitarianism as a universal ethical theory is problematic in several ways, but one issue that is specific to Mill’s conception is brought about by his categorical privileging of certain pleasures over others. I think it is telling that he does not state, specifically, what the highest pleasures are (which, as an objectivist, he should be able to do), but instead gives the rule that “those who are equally acquainted with and equally capable of appreciating and enjoying [any two pleasures] give a marked preference to the manner of existence which employs their higher faculties.” If Mill’s theory is correct, then we would surely be able to elucidate what higher pleasures there are, which use higher faculties, by simply asking people.
But this rule’s efficacy is highly questionable. It is easy to imagine someone equally acquainted with baked apples and Bach, and who has both taste buds and ears, who nonetheless prefers the simple tastes of brown sugar, cinnamon, and butter to dense, precise counterpoint, despite the latter requiring his higher faculties. It is also just as easy to imagine another person, equal in acquaintance and sensory ability, who hates apples and loves Bach. Mill could argue that this is impossible, that, the person who prefers baked apples must really be less capable of appreciating baroque music, for example, but then all he is saying is the tautology that people like what they like. In that case, if there are objectively higher pleasures, then they are subjectively indiscernible, and his rule is, again, useless.
Further, if we are to grant that we can discern higher pleasures, and these are the ones that employ higher faculties, as Mill suggests we will find, then we run into some concerning results. Take the act of eating baked apples again. Does it employ higher faculties? Rationalization? Planning? Not really. An animal can enjoy food just as much. Compare this with carrying out a genocide. You would certainly need a plan to have any success. Rationalization, though probably with deranged premises, would also probably come into play. Yet I think it is safe to say that two people with equal acquaintance would nearly universally consider apples to be more pleasant.
Of course, utilitarianism as an ethical framework would never actually support genocide, would it? Killing a large group of people would certainly cause a large deficit of happiness, since those people are no longer able to experience it. But say those people have some cognitive disability that prevents them from enjoying “higher” pleasures, and that the commission of genocide is, as described before, a higher pleasure for at least one person. Because of Mill’s categorical separation of pleasures, that one person’s pleasure trumps all of the enjoyment he prevented. To be fair, in practice, making choices that tent to create more pleasure is usually simple and effective, but be wary - taking the principle as a fundamental fact can lead to major problems.