Vigilante shooting:
Vigilante shooting should be discussed in 2 forms, limited and unlimited shots.
I'm going to consider positive impact on town based on how it improves win-chance in a random lynch game with random shots. There are no real random-lynch games. A vig-shot is only slightly more likely to hit scum than a lynch is, and if you never lynch a claimed vigilante then they're equal. There are 2 things that work against vigilantes usefulness, neither is considered in a random game, so I'll discuss at the end.
limited shots:
You really need to pay attention to parity. Especially if no other parity-changing rolls exist (i.e. outside of you there will be 1 death every night). A 1-shot vigilante is essentially a 1-shot lynch which only you control. This is a wash for town (as long as they no lynch, and never lynch a vig). But it puts a lot of power into a single players hands.
If you have 2-shots, then you can actually increase the number of town-controlled kills going on, as long as you use both shots. If you can only use one shot, it's a wash. If you use both shots, you increase the number of town-controlled kills by 1. 3-shots is like 2-shots, with the 1-shot vig-lynch. 4-shots or more is basically unlimited.
unlimited shots:
Again parity is key. Half of your shots are just stealing a lynch. The other half are actual bonus kills. Thus you should shoot every night to maximize the bonus kills. If there are other parity-influencing roles then all the more so, since your lynch-steals could actually end up being kills.
Now let's talk about the two things that work against vigilantes.
1. Lynch-stealing. A vigilante is stealing lynches from the town. Some people REALLY REALLY don't like that. If you never lynch a vig it's a wash. If you lynch vigs then it's better for the vigilante to shoot. However, there is at least 1 major concern here: the player isn't warned ahead of time. This can lead to the vig killing your cop, which is terribad. This is ultimately the biggest argument I am willing to concede against the vigilante. Killing power-roles = negative utility. IMO no one should ever try to look scummy, but even more so in a game with a vigilante.
2. Game Acceleration. A vigilante accelerates the game. With extra kills flying around, the game will end sooner. If you think that late game reads are better than early game reads, then this is a BAD THING. Arguably, as the game goes on reads get better and you're more likely to kill scum not just because of having a smaller pool to choose from, but because scum has had more chances to slip up. I'm not sure if this is the case, and would be some good stats to have. Are scum-lynches more likely than average later in the game? (anyone know?) If the delta from average increases (fairly substantially) as the game goes on, then in fact vigs might should hold their shots. It would have to be greater than an extra town-directed kill though.
Alternative Vig Uses:
A vigilante in an open game is a 100% Innocent Child. When he claims, if someone counter-claims, then town can no lynch (or lynch elsewhere), and he can kill the counter-claimer. He probably dies himself which is just what an IC would do.
Note that if there is a doctor or the like, the vig can do this, and still do vigilante-type things too. He's an IC that can kill scum in certain situations.