A vigilante reacts in two ways, he can act on behalf of the established law when no law enforcement is around, or he reacts on behalf or a moral conviction.
The Criminal Justice system is made of 3 parts. (Courts, Enforcement, correction/rehabilitation) a vigilante can only perform Enforcement, and in part correction.
Vigilante implies that that person knows what is morally right or legal. The situation becomes complex when we are defining what is justified on part of the vigilante's right to enforce/judge.
Justice System is developed off years 'democratic' consideration for the various offences that exist, whereas a vigilante reacts only to a law of himself. If ONE person has the right determine what he or she thinks is necessary to punish, then ALL PERSON INDIVIDUALLY have this same right.
DO you see where issues can arise without the justice system?