Religious corruption
This is ironic in general, because the juxtaposition of religion, which classically represents the moral and the incorruptable, with immorality and corruption should leave the reader a little jarred. However, anyone who knows about Brown realizes quickly that Angels & Demons religious perspective will be littered with religious men interacting with nefarious forces and broken vows.
The minor premise irony
In fictional structure, the opening scenes in mystery are typically offered as a hook, usually revealing the fingerprints of some unknown, mysterious force. That means that the opening is usually only related to the plot tangentially, but in Angels, the minor characters from the front of the novel account for major plot details in the rising action of the book.
This structural irony is employed to provide believable plot twists without compromising the continuity of the plot. If the reader feels as though anyone at anytime could be the mysterious bad-guy, they might be disinclined to engage the story, but the reincorporation of the minor plot into the major plot makes the book more believable and more complex.
The irony of Illuminati clues
The Illuminati is a secret society, so it might be advantageous for them to not leave glaring clues about their existence/involvement. But, in Angels, the Illuminati brands the first victim with the word Illuminati, which does not scream "subtlety." But this is an ironic aspect of their position as an organization. They want to effect change in a way that is meaningful, which means that their means must be quiet enough for them to be stealthy, but loud enough to make their point.
The irony of antimatter
Antimatter as a symbol in the novel raises interesting implications about the relationship between religion and science. Antimatter not only represents a very theoretical physic, it also represents a truth that is highly esoteric. Only few people can understand the science that warrants antimatter as a true concept, and yet antimatter is understood to exist, even though most people don't directly understand it past a vague theoretical level.
It's close juxtaposition to the western Mecca, Vatican City, might provide insight into the nature of religion. Some interesting implications are that antimatter might belong in a religious system. Theoretical physics might have broad, conclusive implications in human religion, likening the way we believe in unseen physics to the alleged weakness of religious warrant and belief.
The irony of the tape
The tape itself represents a symbolic irony--that a private, esoteric agenda is made available to the reader and suggestedly the public within the fiction. Another layer to this irony is that the tape reveals a major key to understanding the complex plot, resulting in the failure of the agenda the tape reveals.
When Ventresca is exposed as having killed the Pope along with his involvement with the terroristic secret society Illuminati, it is made apparent that he might still have a legitimate chance at acheiving the papacy, but instead he is consumed with guilt and burns himself in public. But the tape doesn't make him any more culpable than he was before, meaning that his guilt stems from his private agenda becoming public. For this, a revelatory tape is a good symbol and involves many levels of ironic fallout.
