Bourgois's name
Bourgois's name is deeply ironic because it is literally a cue for how the neighborhood should regard him, but to him, it's just a name. The dramatic irony is that the reader can know way more about his character traits than he knows, because the reader might understand the political theory behind the word. In short, Bourgois's name is a signal to his privilege, his superiority complex, and his blindness to his own privilege. Everyone sees it—except him.
The ironic "respect"
Bourgois thinks what he's pursuing is respect, because he wants to be highly regarded and he wants to fit in. He has an ironically low opinion of respect. Many of these community members have their human rights violated regularly, and they are treated by the legal system as menaces, even though many of the problems that face the culture stem from systemic injustice. To them, respect means being treated like a human, but to him, the word is ironically empty.
The drug trade
The idea of drugs for recreation makes sense to Bourgois from a business standpoint, but it is hard for him to piece together the ironic truth about the drugs and the drug trade: It is a style of exploiting the hopeless, because many people use the drugs to face the brutal hopelessness of their life, and then once addicted, stay addicted and depend on the substances severely. It isn't for fun that people are addicted to drugs. He has to learn this through experience.
Violence and intensity
To Bourgois, the violence and intensity of gang warfare comes as a shock, which is a creative use of dramatic irony, because the irony points to his priviege. Of course he doesn't understand the violent intensity of gang warfare. To him, it seems like one thing, when in reality is something way different. He thinks it is for fun and profit, but for many, it is literally warfare, and many in El Barrio treat the police as a pest and the gangs as the true law. To those people, it's not "kind of" war. It is war.
The irony of escape
The plot itself is an ironic inversion of the hero's journey. The "white savior" complex comes under severe scrutiny, because Bourgois views his experiment as a hero's adventure, trying to get a taste of a life that he only fetishizes because he's curious about it, but when he's done, he just leaves. Yes, he comes away with a deeper understanding of the problems, but El Barrio continues on in its brokenness, and he doesn't actually understand what it's like to feel trapped, because he isn't trapped.
