Kersey's work brings him to Arizona, where he learns about the wild west and how to shoot with a gun. On his return to New York, he receives a gun as a gift. So what is wrong, when Kersey defends himself and shoots his attacker with that gun? However, it becomes a habit. Kersey then deliberately puts himself as a bait and shoots whoever want to harm him.
The NYPD must treat those unnatural deaths as homicide and they begin to investigate. On the contrary, those on the political side are happy with the vigilante action as the crime rate is down by half and the New Yorkers start to learn to defend themselves. The crime rate in the movie is so worrying. In a scene in a subway train, we see that a police/guard disappears after seeing 2 muggers approaching; he gives them liberty to do what they please.
It's interesting that Kersey never catches the 3 muggers who have killed his wife and raped his daughter, for he doesn't know who they are. [In 1974 they didn't have CCTV.] It sorts of giving this movie a bit reality, not like some revenge movie. Kersey is also described not as a cold blooded robot who shoots muggers for only revenge. He only shoots those who are attacking him. After his first killing, he even gets sick.