The point of view in "Harrison Bergeron" is third-person omniscient. This is shown by an unseen narrator who is not involved with the story, but knows the characters, their actions, and their internal thoughts and motivations. No character in the story is involved in the telling, and the narrator seems to have knowledge of the story, its origins, and its consequences, as if he were a fly-on-the-wall in multiple locations at the same time.
And it was in that clammy month that the H-G men took George and Hazel Bergeron's fourteen-year-old son, Harrison, away.
It was tragic, all right, but George and Hazel couldn't think about it very hard.
(Vonnegut, "Harrison Bergeron," tnellen.com)
While the majority of the story takes place in the Bergeron's living room, where Harrison's parents are watching the television, the narrator shows knowledge of events outside the room. It is arguable that the narrator may be third-person limited, as everything that happens with Harrison is shown on the television set, but the beginning of the narration shows at least one event outside that scope: the kidnapping of Harrison Bergeron, after the establishment of the Handicap Laws.
Kurt Vonnegut's 1961 satire on popular science fiction depictions of futuristic dystopian societies, Harrison Bergeron, is written from the perspective of an anonymous, unseen narrator. All text is presented in the third person, as in the following description of the story's protagonist, 14-year-old, 7-foot tall Harrison after the government has forced him to conceal his physically and mentally superior attributes for the purpose of enforcing polices on equality. In addition to having to wear a red rubber ball on his nose, he is forced to shave off his eyebrows and wear black caps on his teeth, all in the interest of making his physical appearance less attractive and more in line with that of the masses:
"The rest of Harrison's appearance was Halloween and hardware. Nobody had ever born heavier handicaps. He had outgrown hindrances faster than the H-G men could think them up. Instead of a little ear radio for a mental handicap, he wore a tremendous pair of earphones, and spectacles with thick wavy lenses. The spectacles were intended to make him not only half blind, but to give him whanging headaches besides."
Harrison, of course, has been forced to obscure his physical attributes to ensure that he does not elevate himself above the average citizen. The headphones are intended to interfere with his ability to formulate thoughts, and physically stronger or faster individuals are required to wear heavy weights to slow them down to average speed and weaken them. In addition to the third-person descriptions of characters and actions, Vonnegut's story describes dialogue from the perspective of the unseen narrator:
"'I am the Emperor!' cried Harrison. 'Do you hear? I am the Emperor! Everybody must do what I say at once!' He stamped his foot and the studio shook."