FYI -- I got a freepmail from someone advising me that it probably isn't a good idea to speculate about the mental health of a wealthy, powerful public figure. I have e-mailed the moderators advising them to read the content of my post and, if they feel it is a liability to FR, to go ahead and pull it. So don't be surprised if this thread disappears.
Gibson hasn't been convicted of anything, but fom his own apology its unquestioned that he said anti-semitic and sexist things to the police officers. Since mental illness is less damaging to one's reputation than being a bigot, you're speculation (which I personally think may be on point) is less damaging to his reputation than what he stands accused of being, in fact if he were diagnosed and treated for mental illness he would likely suffer very little career consequences. After all, when A Beautiful Mind came out, the fact John Forbes Nash (wasn't that his name?) was reported to have made anti-semitic statements wasn't held against him, the man was clearly mentally ill.
Neither of us (or at least I'm not) are psychiatrists, but from the way Gibson talks rapidly with darting eyes during interviews, he does seem manic. He wouldn't be the first artist who's form of madness was part and parcel of his artistic genius. But it could be our speculation is wrong and he isn't mentally ill and he's really just a drunk bigot. As a lawyer, I don't think Gibson is in a position to sue you or anyone for suggesting something that only makes him more sympathetic.
He's not quite libel proof (a heinous character, say a convicted murderer, can't sue for libel because his reputation is already so black nothing slanderous would make him worse than what he's already acknowledged to be) but he's too close to it to ever win a lawsuit on the basis of speculation of his mental health.
On top of that public figures almost never win libel suits because the burden of proof is much higher than it is for ordinary people.