In Chapter 26, after Yossarian's first injury in Rome, he and Dunbar move from bed to bed in the hospital, impersonating other patients, in order to continue lying next to each other. After earlier impersonating Dunbar to Major Sanderson, Yossarian finds himself in the bed of a man named Fortiori. Sanderson, frustrated and believing that Yossarian really is Fortiori, wants the man in front of him to stop the nonsense. In Sanderson's scolding, there is an instance of dramatic irony:
You'd better get a grip on yourself before it's too late. First you're Dunbar. Now you're Yossarian. The next thing you know you'll be claiming you're Washington Irving. Do you know what's wrong with you? You've got a split personality.
Dramatic irony is when the audience knows something certain characters in the scene do not know. Here, the audience, having read the first 350 pages of the book, knows that Yossarian has already called himself Washington Irving while he was censoring letters and will continue to refer to Irving throughout the novel. (Washington Irving was an American biographer and short-story writer who flourished in the early 19th century; he is known for the stories "Rip Van Winkle" and "The Legend of Sleepy Hollow.") This dramatic irony continues later in the same chapter, when the narrator notes that the CID men were "after a forger named Washington Irving" and continues through subsequent scenes. This links, notably, with a larger theme in the novel of a lack of literacy among the officers.
This is a quite different type of irony than the type that Heller tends to use much more extensively throughout the novel: that is, situational irony, in which there are indications that a character will act in a certain way, and then they act in a different way. Those sort of contradictions are fundamental to the illogical structure of the novel. The dramatic irony in the quote above, though, is also characteristic of Heller's novel. The non-linear timeline and abundance of characters leads naturally to these moments of dramatic irony.