Let me build on Ken's post below. Donald argues,
"Generally I agree, and I totally agree pre-publication or pre-showing. But what if the movie was made with the intent and specifically funded to foment violence by getting others riled up enough to commit illegal acts, including murder, that you knew would happen as a result of distributing the film? If prosecutors could prove a nexus of this film to a plan or plot, the First Amendment right might not be defense."
As this is a rare instance of comity among SDP commentors, I hate to bicker, but let me disagree slightly with Donald. I am not sure intent is the right measure. If I make a video of myself eating a pork chop and my intention is to offend Muslims and Jews, does that mean that my video can be banned? But if I make the video just because I like pork chops it can't be banned? This looks a lot like viewpoint discrimination.
I will readily admit that this is not my area of expertise, and I am surprised that the legal blogs, especially Volokh, have not really tackled this issue from a legal standpoint (although Eugene Volokh himself, one the the nation's leading 1st Amendment scholars, makes a prudential argument against banning offensive videos here). But it seems to me that there has to be some real incitement in any work in order for it to be banned. Schenk, as Ken alludes, was actively encouraging people to disobey the law. It needs to be noted, though, that "clear and present danger" was largely replaced with "imminent lawless action" in Brandenburg v. Ohio. Does the contents of "The Innocence of Muslims" actually encourage people to violence? From what I have seen the answer is most definitely "No." No reasonable person could draw that conclusion. But, of course, the fanatics are not reasonable.
In the law there is a notion of the "heckler's veto." Just because someone does not like a kind of speech doesn't mean they get to veto it. Example, if I say that every time Barack Obama talks about the killing of Osama Bin Laden I myself will kill someone, does that mean that Obama is inciting violence when he talks about Bin Laden, and thus the law can shut him up? Of course not. The heckler does not get to shut down otherwise protected speech that he doesn't like by making threats. Indeed, as Volokh points out, this would only encourage people to violence. If my preferred view point is not winning, I can just start killing people and then those who disagree with me or have different views must shut up. In American law Muhammed is not sacrosanct. If people want to depict him in violation of Muslim sharia, they are free to do so. If they want to make fun of Muhammad, as, say, Jesus is every day in a thousand different ways, then that is protected too. "The Innocence of Muslims" might be stupid, but it is protected speech. We should all be angered that one of its creators is being hauled into interrogation in the dead of night to answer for this thought crime.
Update: I edited a couple typos from the original.