The Mayor of Rome, Wisconsin, a town approaching Starnesville status, is one of the first people that Hank and Dagny track down regarding the Motor Factory. While the mayor puts them on the trail of Eugene Lawson, who plays a considerable role in the book later on, that isn't his most important role. The Mayor becomes significant at the end of his one scene, when he notes that Dagny isn't Hank's wife:
Dagny saw Rearden's face go white..."Keep your dirty –" he began, but she stepped between them.
. . . Mayor Bascom looked astonished by Rearden's reaction; he had made the remark without malice, merely like a fellow cheat displaying his shrewdness to his partners in guilt. "Lady, I've seen a lot in my lifetime," he said good-naturedly. "Married people don't look as if they have a bedroom on their minds when they look at each other. In this world, either you're virtuous or you enjoy yourself. Not both, lady, not both." (18.104.22.168-41)
The Mayor gives us insight into how society would view Hank and Dagny's affair. These views also echo the ones Hank spouted off, and possibly even recited, to Dagny the morning after they first slept together. Dagny uses this incident to ask Hank to reconsider his own views.
Hank comes away from this incident feeling guilty and protective of Dagny, which is a character trait that comes back in spades when he is confronted with the Gift Certificate blackmail. Though Hank's views evolve and become different from those held by the Mayor, his protectiveness of Dagny seems to intensify as the book proceeds. This scene is notable for being one of the first instances where that aspect of Hank's character emerges full force.