The simple answer is "no," for all the very good reasons cited above. An acceptance of extra-judiciary killing would mean an abandonment of civilization. I've been reading a book lately about the jury system in the seventeent century, and I've been struck by how seriously jurors even then took their obligations. The legal system (despite any and all lawyer jokes) is something to be proud of.
I think that if a society determines that some of its members need to be killed, either in punishment or because they are too dangerous to be left alive, then there needs to be a government-sanctioned process for doing so. The exception to this is self-defense.
A society that allows extra-judicial killing is opening its doors to complete chaos and anarchy. It is abandoning the rule of law. If I can kill you because you have dishonored my family, I become the law. I get to decide who should live and who should die. If every person is given this right, we have complete chaos. Therefore, allowing extra-judicial killing invites disaster.
I feel it should not be allowed. In making such decisions, long and short term consequences should be considered.In my opinion, killing is not right which also includes abortion.
In my opinion, no killing should be permitted. No-one has the right to kill one another, and people should have the right to be able to live in this world without the thoughts or worries about being harmed (however, abortion is different in my point of view. I am completely for abortion). In the case of judiciary killing, it is still no exception.