Vigilantism is the exact opposite of law and order, and when vigilantes appear, it is a synpthon of either the breakdown of the law and order of a society, or a perception that it is no longer adequate. This kind of behavior cannot be toleranted, and the root causes need to be treated.
Vigilantism is in some sense a very attractive concept, and almost everyone is attracted to stories of Batman and other people who punish evildoers outside the law. However, if one private person can retaliate against another person, what is to prevent that person (or his/her family) from retaliating in turn? This is how family feuds begin, leading to a massive cycle of violence in which more and more people are caught up. Also, how can a private person always know who has wronged him or her? Perception can become reality, and innocent people can be punished by other people who consider themselves the innocent person's "victims." For these reasons, vigilantism will only result in more violence, much of it lawless and unjustified.