How does the author use dialogue and the events of the plot to reveal characterization and theme in "After Twenty Years"?

Dialogue and the sequence of events in "After Twenty Years" work to reveal the characters of Jimmy and Bob along with the story's theme through the information they provide.

• Dialogue to reveal characterization

In the exposition of the story the initial dialogue between the policeman and the apparent stranger who waits in a doorway for his old friend reveals some characteristics of both men. The stranger has had an arrangement with his friend, whom he terms "the finest chap in the world," to reunite at their favorite restaurant in twenty years. They have not seen each other because he has gone West to seek his fortune while no one "could have dragged Jimmy out of New York."
The policeman obtains more information about Jimmy after he asks if the man has heard from his old friend. The stranger replies that he did at first, but after a year or two,

"...we lost track of each other. You see, the West is a pretty big proposition, and I kept hustling around over it pretty lively."

But, the stranger adds that Jimmy will not forget their arrangement because he is "the truest, staunchest old chap in the world." Then, after the policeman asks if the stranger has done well out West, he replies,

"You bet! I hope Jimmy has done half as well. He was kind of a plodder, though good fellow that he was. I've had to compete with some of the sharpest wits going to get my pile."

This latter part of the exchange between the policeman and the stranger suggests some marked differences between the two friends. For one thing, the stranger's use of words about himself such as "hustling" and his saying he has had to compete with "the sharpest wits going to get my pile" hints at a nature that may possess some criminality because "hustling" and "pile" are part of the lingo of criminals. Frequently, too, he implies a contrast between himself and Jimmy, who he describes as "staunch" and often as "good."

Apparently, the policeman has inferred things from this stranger's conversation because he takes his leave; however, before he does, he asks if the man will call time on Jimmy sharply on the hour. "I should say not!....I'll give him half an hour. If Jimmy is alive he'll be here...."

At this point, a perceptive reader may well wonder why the policeman has asked such a question since he has no part in the meeting. But, it is not until the ironic ending for which O. Henry is famous that the reader learns of the true identities of the two characters. These identities are revealed in Jimmy's letter to Bob.

• Dialogue to reveal theme

With a theme of "After Twenty Years" being that Morality and Duty take precedence over Friendship, the fact that the policeman has not identified himself as Jimmy to his old friend Bob suggests that certain values of the policeman are involved. And, it is the letter Jimmy writes to Bob that reveals this theme of Morality and Duty in which he informs his friend that he is under arrest because the plain clothes policemen pretending to be himself has just made this arrest. Nevertheless, Jimmy has not stopped being a friend as his words in the letter also reveal--"Somehow I couldn't do it [make the arrest] myself...." 
Thus, Jimmy is yet the same as his friend has described him: good and "the truest, staunchest old chap in the world" because he has been at the meeting spot on time, and he has tried to save his old friend embarrassment.