What I don't think it was is "justice". It was revenge. Which is, in it's way fine. A lot of people feel better now. Ok.
But justice, justice would be him in chains, in court, the evidence for his deeds laid out, and a chance for him to rebut them made available.
We begin with the ongoing – stereotypically left-wing – confusion between the war model and the law enforcement model. In the war model, Osama bin Laden (OBL) is considered to have declared war on the US, and prosecuted it. This has been his declared intention, and the war model merely takes him at his word. In war, soldiers are allowed to kill the enemy. There is no presumption of innocence because war is not a crime, at least as long as soldiers observe certain rules. Soldiers who surrender can be detained in prison camps without trial, because the purpose of detention is to keep them from prosecuting the war. You don't need to prove the soldiers were at war, because they declared themselves to be at war by, among other things, wearing the uniform of their country's military.
Now, under what circumstances can an enemy soldier be summarily shot on sight? (Let's assume the worst possible case -- he was offering no resistance.) Hugh Hewitt raised the question with "The Smart Guys" on his show. John Eastman pointed out that under the Geneva Conventions, OBL would be considered an "illegal combatant" and therefore subject to being shot on sight. I had to turn off halfway through Eastman's response, so I never heard Chemerinsky's point. I'll have to pull up the podcast. Nevertheless, at least one law school dean opined that the summary execution of OBL was perfectly legal. I think that's enough to consider it an open question.
In the law enforcement model, you have a presumption of innocence because it hasn't been established in court that a person has committed a crime. In this case, it's appropriate to administer Miranda warnings, and other Fourth Amendment and Fifth Amendment protections apply. Treatment of a criminal is distinct from treatment of a war prisoner, in that the object is punishment and not mere restraint. And even that occurs only after a judicial finding of guilt. Certainly, summary execution is not allowed under US criminal law.
The second thing I noticed was a distinct lack of excoriation. Obama receives much more gentle treatment than Bush ever did. Gone are the vitriolic adjectives heaped upon Bush and his administration. The most he says about Obama (on a slightly-related topic) is:
That's the sort of thing which makes me wonder if he deserves to be president, because it's the sort of thing I complained about his predecessor doing, and it's no different when Obama does it than when Bush did it, or some tinpot dictator does it somewhere else.
In other words, he still supports Obama, gives him the benefit of the doubt, and will need to be talked out of supporting him. He never supported Bush, gave him no such benefit, and considered him evil from the get-go.
This is his political bias, and he's certainly entitled to it. But it's essential to keep this filter in mind while reading his posts. They are not unbiased down-the-middle reporting.