Let us recall that the definition of irony is the gap between appearance and reality. Clearly, therefore, Walter Mitty with his repeated day dreams that occur throughout the story and then his real, hum-drum life where he is constantly nagged by his annoying wife, represent opposite poles of the kind of life Walter Mitty would like to live and the actual life he has to live.
Let us just briefly examine the daydreams that Walter Mitty has. In each, he is a charismatic, vibrant man who is daring, brave and courageous. He is able to inspire the confidence of those around him. In the first daydream, for example, when the commander Mitty heads the plane straight into the storm (a suicidal move, pure action hero nonsense), the crew of the plane have absolute confidence in Mitty:
The crew, bending to their various tasks in the huge, hurtling eight-engined navy hyroplane, looked at each other and grinned. "The Old Man'll get us through," they said to one another. "The Old Man ain't afraid of Hell!"...
The key word for these daydreams is significant. Through this escape, Walter Mitty becomes a significant individual. This is of course in sharp contrast to his actual day to day existence. Consider how his wife treats him and also how Mitty thinks of their relationship:
He looked at his wife, in the seat beside him, with shocked astonishment. She seemed grossly unfamiliar, like a strange woman who had yelled at him in a crowd. "You were up to fifty-five," she said. "You know I don't like to go more than forty. You were up to fifty-five."
It is clear that Mitty's wife has him under her thumb, and her manner of repeating herself and her complaints twice makes her particularly irritating.
Clearly, then, there is massive irony in Mitty's character. His monotonous existence forces him to live the life he thinks he would like to lead in his daydreams - and here lies the central irony, for in some ways, his reality is less real than his daydreams.