Where's the legal authority for the Government to buy AIG?
Nowhere, but apparently not enough people care.
David Zaring:

But, in the Fed's legal defense, maybe, just maybe, the settled expectations are different here, based on the government's takeovers of Fannie and Freddie, and the pleading by AIG for government involvement. Does the very fact that the insurer hoped for Fed action suggest that the Fed could act?
Hmmm. The other defense would be that emergencies are emergencies, and when that happens the rules go out the window, and hopefully regular elections mean that the officials the people trust are dealing with the emergency. Abraham Lincoln adopted that reasoning, and he won the Civil War. I suspect we're at the "anything goes in an emergency" stage of things. But maybe reasonable minds could disagree.

Megan McArdle writes,

A lawyer friend IMs "I would be fascinated to know on what authority the Fed is claiming the right to do this." It's probable that they don't actually have the legal right to do anything like this. Their authority is this: who's going to stop them? No one wants to take on responsibility for this mess themselves.

I'm all for living in interesting times, but these days, things are getting curiouser and curiouser.