An example of dramatic irony is when the police commit the only sane person in the city.

Dramatic irony is when the reader knows something that the characters do not, and the character’s actions result in something unexpected.  In the story, we realize that the narrator is different from the rest of his society.  People do nothing but stay in their houses all day long, watching television.  There is only one police car because police are not needed.  There is no crime.

The pedestrian is what we would consider normal.  He is taking a walk at night on the deserted streets.  As he passes the houses, they look like a graveyard.  Metaphorically, society is dead.

When he is stopped by a car, the pedestrian considers his bad luck that in such a large city the one car has found him.  The car takes him to the “Psychiatric Center for Research on Regressive Tendencies.”

They passed one house on one street a moment later, one house in an entire city of houses that were dark, but this one particular house had all of its electric lights brightly lit, every window a loud yellow illumination, square and warm in the cool darkness.

The pedestrian is considered insane because he is not like everybody else.  He behaves in a way we would consider normal in our society, and other people behave abnormally to us.  Thus the reader realizes that committing the only sane man in the city is ironic, even if the cops do not.

Bradbury often depicted technology as the downfall of society, and individuals that tried to make human connections were targeted.  The story is a warning to all of us not to get taken in by what may seem easy and interesting.  We need to maintain our humanity.

For more:  http://www.enotes.com/topics/literary-terms/in-depth (please see "irony")