Let us remind ourselves that situational irony is based on plot, and is the term used to describe a sudden twist in the course of events that makes the precise opposite of what we expect to happen occur. A classic example would be a rags-to-riches story in which a poor person suddenly becomes rich at the end.
If we examine this term in relation to this excellent tale, we can see that the situational irony relates to Harrison Bergeron's sudden appearance on the TV show and how it is dealt with. The way in which Harrison bursts onto the show, crowns himself Emperor and takes one of the dancers for his Empress, then proceeds to dance in a way that defies gravity itself, leads us to believe that he will mount a successful revolution against handicapping and end this era of forced equality and no competition. It is therefore a great shock and surprise to us when this ending does not occur, and the dance is rudely interrupted:
It was then that Diana Moon Glampers, the Handicapper General, came into the studio with a double-barreled ten-gauge shotgun. She fired twice, and the Emperor and the Empress were dead before they hit the floor.
The grim situational irony of this story therefore relates to the way in which Harrison Bergeron's revolution is cruelly crushed with his violent and sudden murder, and the change that the story looked to offer us never comes to pass.