One commentator raised a point about the state being absent in New Orleans right now, making it more morally right to act outside the state. I've written about this at length (Miners, Vigilantes and Cattlemen, 33 Land and Water Law Review 581 (1998) - you can get it on Westlaw or Lexis if you have access, otherwise email me and I'll send you a hard copy.)
It is too late to come up with a pithy summary - all I will say at this point is that (1) historical experience suggests that it is actually quite hard to get a vigilante movement going because there are serious free rider problems involved and (2) there were some quite successful vigilante efforts in the 19th century that made dramatic improvements in law and order, most notably in Montana in 1863-64 and the early to mid 1880s but there were also some horrific abuses, such as the Johnson County War in Wyoming in 1892. The difference between the "good" and bad vigilante movements often turned on the relationship with the state. The key point is that there are some important incentive issues involved that make me suspect that there is more likely to be underprovision than overprovision of private efforts at law enforcement.