First, let's make sure of the definition of dramatic irony - a situation in which a statement by a character in the story carries more than intended significance for the audience which has insight or understanding that the character doesn't possess.
In Harrison Bergeron, almost every sentence carries dramatic irony. The system of handicapping devices that has been instituted has made all citizens equal by negating any "advantages" some individuals might have had over the "normal" abilities of the population. Hazel Bergeron, as a completely "normal" person, can't truly understand or identify with the impact of her husband George's handicapping measures. In fact, she finds them interesting.
"I'd think it would be real interesting, hearing all the different sounds," said Hazel, a little envious. "All the things they think up....I think I'd make a good Handicapper General....Who knows better then I do what normal is?"
The readers of the story quickly come to understand that the transmissions to George's mental handicap radio are definitely not interesting; they also become aware that Hazel does not have the ability to focus on any one sustained effort or thought in the way that would be required of the Handicapper General.
When the announcer breaks into the television program to announce Harrison's escape from jail, he has great difficulty communicating. Announcers, people whose profession in our culture requires strong and clear speech so as to be understood, in the setting of this story possess handicaps such as speech impediments. This is ironic in and of itself. Hazel's reaction to his attempts to read the news bulletin highlights the irony of his position, given his speaking difficulties.
"He tried to do the best he could with what God gave him. He should get a nice raise for trying so hard."