The irony of indulgence
In a word, Trollope finds America to be indulgent, but Americans celebrate freedom as a virtue, so giving people the social permission to indulge is part of what makes America function. She sees that the culture is not held together be common values and ways of life, but rather, America has become a new kind of cultural organism entirely. The funniest example is how disgusted she is when an American spits his chewing tobacco in front of her company, on his own carpet in his home.
The book's ironic title
The book is not about manners at all. It is a discussion of the opposite of manners, the mannerless culture of America. In her opinion, America's abandonment of English fashions led to a disgusting culture with no manners or politeness. The title is a kind of ironic joke about that basic opinion.
The irony of slavery
In England, they moved away from slavery sooner than in America, and popular opinion changed more radically in England than in America, so when Trollope visits America, she is astonished that people in the American south were still so overtly racist and comfortable with slavery. She viewed this as a side effect of some kind of moral degradation in America, but there are also other historical and economic factors that she doesn't really discuss fully. In any case, she finds the American opinion of that time to be uncalled for.
The irony of American religion
The American church is not historically a traditional one (although traditional religions have always been a major part of our history). The church was just entering the evangelical age when Trollope visited (evangelicalsim is still the main theological movement in the American south today). She found the movement to be troubling to say the least, and she had her reservations about the prospect of "Religious Awakenings."
The irony of American politics
In Trollope's opinion, Americans have forgotten what politicians are for. Instead of hiring the most competent person for the job, Americans often vote for who speaks more persuasively, or who dresses better, or who has a more handsome face. By voting for who they like, Americans have reduced their own power and representation, and perhaps they become more susceptible to political manipulation.
