What behavior in the book might be viewed as abnormal and illegal?
For a reader, someone outside of the book/story, everything that the Handicapper General does seems abnormal and should be illegal. This story is a dystopia. That means it presents a dark vision of the future. Often dystopias involve a loss of individual freedom for the majority of citizens. To the reader, this kind of oppression and limitation of people's freedom and abilities is outrageous and should be illegal.
Within the context of the story, it is quite the opposite. Anyone who dares to act or even think in a way that might make them superior to other citizens is deemed illegal by the government and the Handicapper General. It is 2081, and the 211th, 212th, and 213th amendments have enforced equality across the board. If a person has some advantage in looks, intelligence, or physical ability, he/she is given a handicap so that he/she is equal to everyone else. It is therefore illegal to be better than another person in any way.
Harrison's father, George, is quite intelligent. To bring him down to the level of average intelligence, he is given a mental handicap in the form of a radio in his ear. Any time he starts to think above the level of an average intelligence, a signal is sent to his ear to distract him. It would be illegal for George to take the device off. George is also burdened by a forty-seven pound sack of bird shot. When Hazel suggests he take it off, he says it isn't worth it. "Two years in prison and two thousand dollars fine for every ball I took out," said George. "I don't call that a bargain."
In this dystopian world, everything Harrison does is illegal. His physical and mental abilities are so great that he's given the most burdensome handicaps the government has available. But they can't hold him. In a moment of rebellion, albeit mostly selfish, Harrison sheds his handicaps and proclaims himself emperor. All of this is illegal because he is proclaiming how superior he is to everyone else. In the world of this story, most people have come to accept that stronger and more intelligent people should be handicapped. To most, with the exception of people like Harrison, handicapping people seems like a normal social practice. They believe, or are forced to believe, that it is for the greater public good.