From simply holding down a robber to things like Batman, vigilantes can help sometimes a lot more then cops can. If say the average cop takes 15 minutes to get to a 911 call, that gives the criminal enough time to rape,steal, murder, etc. But if someone was, say dressed up in a cool looking hoodie and jeans and walked around town looking for crimes to stop, he has every right to be a vigilante hero no matter the law.
The problem is, people will try to be the 'hero' and often commit a crime I'm doing so or make the situation a lot worse than it already was. If a vigilante was to intervene in a situation where for example a mugging was about to occur, then struck the mugger and caused serious harm before the offence was comitted. Would he be a hero or the villain?
Many situations can occur, the outcome in all of these may be perceived differently by society, but all in all being a vigilante and committing crimes to stop crimes is no way to go about it. The world has the hero's it needs in the armed forces and police stations, it doesn't need no wanda be vigilantes causing problems and wasting there time, while putting themselves and the public in danger. You want to be a hero, go join your local police force.
Batman is a comic book character and if he existed modern DNA testing would reveal his identity, which would result in his arrest.
Funnily enough if you watch the Batman the Dark night film, there is a scene where Batman discourages a group of copy cat vigilantes.
In some cases a vigilante can, stop a crime in progress, but it varies for example the average person may be able to tackle a pickpocket even scare off a knife wielding robber at a store.
But taking the law into your own hands against most criminals, could easily result in you getting killed, real criminals are not all like the ones you see in the movies they can and will kill you, in most cases just for witnessing the crime let alone trying to stop it.
Acting like a vigilante can result in you taking it too far and actually committing a crime Eg: beating the crap out of a criminal/or a completely Innocent person , or killing them.
For example, in Australia I heard of a case where a farmer shot an intruder who broke into his house in the foot, rather than killing him. The intruder and the farmer were both charged for different reasons by the police.
If you want to uphold the law apply for the nearest police academy.