Bannion's vigilantism: How did this movie get past censors?

They certainly walked on a fine line, but they did not cross it because the hero himself, Bannion, though he kept on investigating, didn't take the law in his own hands (e.g. execute the law) because he neither killed Larry nor Mrs. Duncan and killing Vince was self-defence (and to protect Debbie) and not presented as vengeance. If he would have killed any one of them just because he wanted to punish them then it certainly would have violated the Production Code but by letting Larry getting killed by the villains, Debbie killing Mrs. Duncan and Bannion only killing Vince in self defence they managed to avoid problems with the Production Code.

You're right, back then there have been only very few films which showed the hero taking the law into his own hands and if he did he had to suffer from it one way or another (e.g. getting killed himself) in order to make it clear that his actions weren't right. In the end people who did violate the law always had to be punished for their actions. Also if people e.g. drank too much they or at least their habit has had to be portrayed in an unsympathetic or some other negative way.

Well, there have been certain times when the Hays Code has been a bit softer on some things, but generally speaking 1941-1955 have been the years when they've been particularly strict (but even there have been some exceptions e.g. in the first few years immediately after the war more brutal portrayals of violence - e.g. in 'Brute Force' - were allowed).

Ah, the Hays Code...a topic that could be discussed endlessly. 

First, I think people nowadays understand the Code quite wrong. They think that portraying and talking about things like sex, adultery, pregnancy, prostitution, homosexuality and so on was completely forbidden. This was not the case at all. Yes, if you look up the Code in its entirety it must seem that way, after all the Code is a long list of "don'ts".

But pretty much everything that you see on screen nowadays you could also find in old movies. Implying things, as opposed to actually showing them, was fine. The censors were concerned with blatant display of sex, violence, vulgarity etc. Emphasis on blatant. There was nothing in the code that said sex or even homosexuality couldn't be hinted at or alluded to. Old films basically relied on hints and secret winks to the audience to get the idea of some naughty idea across. The audience just had to pay a bit more attention and read between the lines.
I've seen many Noir films and can definitively say that there are so many twisted, odd and sick stories there, I very often wonder what makes people think old movies are "innocent".

So maybe the Code stated EXPLICITLY that the hero of the film should not take the law into his own hands, but if the censors had always strictly applied what the Code preached, literally hundreds of great movies could not have been made during that time. You can easily find racy dialogue (The Big Sleep), steamy love scenes (Notorious), sexual obsession (Postman), more or less hidden homosexuality...

Also, Moscoso is right in saying that Bannion did not really cross the line into outright vigilanteism. He did not kill anyone in cold blood. That, and only that, would have been a problem under the Code.

Just a few years later Dirty Harry could go around and torture suspects and hand out what was definitively vigilante justice without being held accountable, Bannion could indeed not go quite as far under the code.

Jessica Rabbit
"I'm not bad. I'm just drawn that way."

While the Hays code may have supposedly forbidden various subject matter. The main items of enforcement were nudity, sex, and curse words. The morality of the plot was much less a concern. The rogue cop doing the right thing was a fairly well used plot mechanism. This film is not a rarity in that regard.