Of course, the central irony of the story is that a simple activiity—walking—is considered abnormal in the dystopian society of Bradbury’s story. This “normal” habit of walking the deserted streets is “regressive,” suggesting some previous time when people routinely walked for pleasure.

Another source of irony is the fact that there is not much difference between the darkened houses Mead passes in 2053 and the darkened houses one would pass walking at night through a suburban neighborhood in 1951 (when the story was written) or 2018 (when this is being written). The image of people disconnected from each other and the outside world, their sense of reality mediated by television, is hardly one that requires science fiction.

But I suspect that the real irony of the story centers around the idea of writing itself. Mead identifies himself to the police car as “a writer,” which the police car decides means “no profession.” Mead silently agrees: “He hadn't written in years. Magazines and books didn't sell any more. Everything went on in the tomblike houses at night now, he thought, continuing his fancy. The tombs, ill-lit by television light, where the people sat like the dead, the gray or multicolored lights touching their faces, but never really touching them.” In a way, Bradbury’s writing of the story is a kind of refutation of Mead’s contention that “magazines don’t sell” (i.e., Bradbury himself is a writer, and the very text in which Mead appears would seem to refute his claim that writing isn’t possible or lucrative). But there is also a sense in which Mead’s nightly walks are an attempt to gather material for writing, material which is not forthcoming or accessible. It’s ironic that Mead is picked up for this activity, since it is truly harmless (Mead likely will never write anything). It’s ironic that the stories on television, which so absorb the townspeople, are the things that inhibit the human interactions that make stories (and writers) possible.

It's a little tricky to identify irony in Ray Bradbury's "The Pedestrian," but there are a few interpretive claims you might make if you need to identify that particular literary device.

Situational irony occurs when the opposite of what we'd expect happens in a particularly interesting or critical way. For example, it would be situationally ironic if the firehouse (the building belonging to the people whose job it is to put out fires) burned down.

You might argue that it's ironic that Leonard Mead continually thinks of the urban landscape he wanders in natural terms:

The street was silent and long and empty, with only his shadow moving like the shadow of a hawk in mid-country. If he closed his eyes and stood very still, frozen, he could imagine himself upon the center of a plain, a wintry, windless Arizona desert with no house in a thousand miles, and only dry river beds, the streets, for company.

Mead's thoughts paint a picture of a city being reclaimed by nature, with sidewalks "vanishing under flowers and grass." He uses this to emphasize the lack of a human presence in the city at night; people sit at home and watch television instead of going out or visiting friends. This is ironic because in Bradbury's vision, the industrialized, technological future actually leads humans to abandon their environment and make less of an impact on the landscape—the opposite of what we might expect. In short, our expectations about what progress should look like are reversed; this vision of progress looks like decline. By the same token, humanity's unnatural technological advances actually cause nature outside to flourish (the opposite of what we would predict).

It’s also ironic that the man we as readers identify as the most normal character in the story—the one who doesn’t want to sit at home and watch TV every night—is regarded by his society as deviant to the point of criminality: at the end of the story, he is taken away to the “Psychiatric Center for Research on Regressive Tendencies.” Though we regard Leonard Mead as natural (both in his behavior and in his affinity with the natural world), his society sees him as unnatural—the exact opposite of what we might expect.

What is an example of dramatic irony in "The Pedestrian" by Ray Bradbury?

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")