Well it all boils down to millenia old question - who guards the guardians? It starts off as a nice concept of swift justice not hindered by beaurocracy but it seeing as how it is above the law there are no restraints and eventually things will go south and people WILL abuse their liberties to their own ends whether their maniacal lust for slaughter or just seeing everybody as collateral - would you bomb a terrorist house if his wife and kids are in the house? And ofcourse without the slow justice system doing its cumbersome work some rush judgement call are bound to be made, so a scapegoat is killed there or the small fish take the heat for the entire crime organisation and so on. It is big shiny tasty looking apple that is completely rotten on the inside and once you take a couple of bites, you realise that.
The more interesting issue however is how they would deal with their stealth - you take out big people you are bound to pull attention to yourself. A secret that is known by two people is no longer a secret. I would suggest relying heavily on middle men to do the dirty work - hitmen for hire that dont know who they are working for and are paid enough never to ask questions - but that's not exactly story material i guess cause the heroes constantly change...
The more interesting issue however is how they would deal with their stealth - you take out big people you are bound to pull attention to yourself. A secret that is known by two people is no longer a secret. I would suggest relying heavily on middle men to do the dirty work - hitmen for hire that dont know who they are working for and are paid enough never to ask questions - but that's not exactly story material i guess cause the heroes constantly change...