In "The Secret Life of Walter Mitty," the parody lies in the characters that Mitty creates in his daydreams. His heroes are extraordinary, skilled, super-hero type people, they are so over the top that the author seems to be mocking these type of people. Either they don't exist, or if they do, James Thurber is mocking them in this work.
Mitty's alter egos in his fantasies are exceptional, they are superhuman in their abilities to confront conflict and solve problems. Cast against the hapless real-life Mitty, the story is funny, or comical when you think that Mitty, in his everyday life can't remember what his wife said to buy at the store. He fantasizes about being these larger than life type heroes, who next to him, make him look like a fool.
Thurber mocks Mitty in two ways, first, he is juvenile in his quick escape from real life. Having daydreams at his age, either Mitty is insane or mentally unstable or suffers from delayed development and remains emotionally a child. He wastes his time on daydreaming rather than making something with his real life.
Also, the sound effects used in his scenarios, such as, pocketa, pocketa, pocketa, which is the same for the airplane as it is for the fancy machine in the operating room. Linking the daydreams or fantasies together with this sound effect acts as a parody in that it mocks the different characters that Mitty assumes through the continued use of this sound. The sound effect is silly and unrealistic, so we know that Mitty is in another daydream, not a memory.