In Section 2, the anxiety provoked by the arrival of the mysterious sack of gold in Hadleyburg—which has elicited feelings of overwhelming greed among the village's nineteen prominent citizens—hangs over the entire town. Jack Halliday, a wise-cracking local who "always noticed anything," and who speaks for the rest of the town as they watch the ridiculous behavior of the nineteen, is quick to observe the change in the air. He uses hyperbole to get his point across:
[Halliday] began to throw out chaffing remarks about people not looking quite so happy as they did a day or two ago; and next he claimed that the new aspect was deepening to positive sadness; next, that it was taking on a sick look; and finally he said that everybody was become so moody, thoughtful, and absent-minded that he could rob the meanest man in town of a cent out of the bottom of his breeches and not disturb his revery.
According to Halliday, the gloom is bad enough to change the ways of even the “meanest” citizen: Halliday could rob him of his precious change and such a citizen would hardly notice. The implication of this observation, of course, is that the town's "meanest" citizen is one of the nineteen local elites who are most affected by the gold and therefore the gloom—despite their apparent virtue and prosperity.
Halliday plays the part of the clear-eyed Shakespearean Fool in "The Man That Corrupted Hadleyburg": he sees the behavior of the Nineteen for what it is, and his perspective—which therefore highlights the contradictions and contortions of the citizens caught between their illusory virtue and their deep-set vanity—provides both the harshest and most humorous instances of satire in the story.
In Section 2, Edward Richards is the first citizen to receive a follow-up letter from a "Howard L. Stephenson." In the letter, this Stephenson details how Goodson had originally made the remark that was so worthy of the mysterious "gold," but adds that Richards—by virtue of some unnamed favor for Goodson—is his "legitimate heir." In a fit of angst, Richards wracks his brain to remember this apparent favor. Perhaps, Richards wonders, he had saved the stranger's life? The reader is, by now, well aware that Richards has no actual claim to the gold, and Twain captures Richard's cognitive somersaults with his trademark satire and hyperbole:
His life? That is it! Of course. Why, he might have thought of it before. This time he was on the right track, sure. His imagination-mill was hard at work in a minute, now.
Thereafter during a stretch of two exhausting hours he was busy saving Goodson’s life. He saved it in all kinds of difficult and perilous ways. In every case he got it saved satisfactorily up to a certain point; then, just as he was beginning to get well persuaded that it had really happened, a troublesome detail would turn up which made the whole thing impossible.
The way Twain has written this passage, Richards spends the evening actually saving Goodson's life, over and over. This hyperbole is a classic method by which Twain teases out satire from his narrative: by his description, Richards's clumsy attempts to prove himself the rightful heir to the gold become even more painful to behold.
This passage is a wonderful example of the thematic conflict between vanity and virtue on display throughout "The Man That Corrupted Hadleyburg": Richards is desperate to claim the money, and vain enough to believe he has earned it—so his only recourse is to fabricate a memory of his supposed virtuousness. Satire is the main—and most effective—mechanism by which Twain lays bare the hypocrisy of this behavior and the behavior of Richards's fellow citizens.
In Section 3, a massive crowd gathers in Hadleyburg to witness the Reverend Burgess reveal the rightful inheritor of the sack of gold. To kick things off, Burgess gives a melodramatic speech in which he waxes poetic about the treasure and the town entrusted with its care. Despite his hyperbolic insistence on the value of the sack and the virtue of Hadleysburg, Burgess's speech fosters a sense of dramatic irony in the reader:
He related the curious history of the sack, then went on to speak in warm terms of Hadleyburg’s old and well-earned reputation for spotless honesty, and of the town’s just pride in this reputation. He said that this reputation was a treasure of priceless value; that under Providence its value had now become inestimably enhanced, for the recent episode has spread this fame far and wide, and thus had focused the eyes of the American world upon this village, and made its name for all time, as he hoped and believed, a synonym for commercial incorruptibility.
By now, the reader knows just how deep the moral rot in Hadleysburg goes—every single one of Hadleysburg's nineteen prominent citizens has laid claim to the gold, a crisis that Burgess will shortly discover. Each new instance of hyperbole in this speech—that divine "Providence" herself has "enhanced" the treasure, that Hadleyburg will become immortal in its reputation of "incorruptibility"—just serves to raise the reader's anticipation of the Nineteen's collapse and the world's realization of Hadleyburg's true nature.
"The Man That Corrupted Hadleyburg" is ultimately a tale of revenge—one stranger's revenge on the town that once wronged him—and by drawing out the climactic revelation Twain ropes the reader along in the stranger's quest. Both the reader and the stranger are outsiders in this story, and they can only sit back and watch as everything begins to collapse.