A very cold emotionless look with a slick grin and a slight sparkle when looking at someone as a victim. You know, the type of look that says creepy.
Look at Silence of the Lamb. Anthony Hopkins had it going creepy all the way in his slightest looks and gestures.

Insanity is wide eyed, fingers clawing and scratching, lower jaw jutting out, drooling, nose curled into a snarl.

That’s an interesting question, but I also believe it’s a tough one to answer. Simply because mental illness has been alienated and turned in to entertainment industy by movie and entertainment companies. You probably will get different answers depending on how influenced people are by this. Schizophrenia is the classic description of insanity, made up by the entertainment industry and people with this diagnose have been wrongfully treated by society thanks to this. Such a shame. Reports are still in the news that if you have ADHD “you are likely to end up a serial killer” (read it somewhere a couple of years ago.

The human mind is fragile. I believe we can all become insane when triggered.

With this said my imagination of someone insane would be pretty much a person like the one @davidbetterman describes.

Ok, sorry, the above answer wasn’t really an answer to your question, but more of an opinion. But the latter part of it is :)

This sounds like body language study for role research.

Maybe they would be fidgety, jumpy, and nervous. Lots of jerky movements, wandering eyes, crossing arms, crossing legs, shaking foot, touching the face a lot, defensive tone of voice. Kind of like that classic (Sweeny Todd type) murdering barber Monty Python sketch. http://www.youtube.com/watch?v=P3IcdxbnIfY

Maybe they would be cold, stoic and callous. This type has a better poker face, is a better liar, would make a better salesman, and is more of the charmer. He’ll wink at you, but get grumpy if you don’t listen. A salesman is actually a good person to study for that, like the over-the-top likeable businessman portrayed by Christian Bale in the zany, surreal American Psycho. http://www.youtube.com/watch?v=qwicLgOGJOI

The two would be two basic versions, and the appropriate one would depend on the character, or actor. In both scenarios, they want to cover something up. Yet they are both showing signs that they are hiding something, so they aren’t doing a very good job.

Christopher Walken says he tries not to get too caught up on details, and just latches on to one basic trait, one twitch, one habit, and goes from there. Someone who acts a little bit different than straight-forward, status-quo comes across on camera as menacing.

Depends on what kind of mental pathology we’re dealing with: depression, schizophrenia , paranoia, split personality disorder… each has its signs…

It is spending over an entire year pursuing a relationship with someone and not knowing why you are doing that!

As a mental health worker my experience of most people suffering from mental health issues is that they are visibly indistinguishable from you or I, most of the time. Almost all of the visible physical symptoms are actually the result of side-effects from medication. Drooling, jerky motion, trembling, the wide-eyed look. If you are wanting to portray real mental health issues you need to do things like, stop washing, stop cleaning your clothes, however as @Thammuz said, it really does depend on the problem the person has.

The Objective Correlative:
http://www.merriam-webster.com/dictionary/objective+correlative

From a practical sense, it’s a behavior the actor uses to evoke an association in the audience’s mind. If the character looks or sounds a certain way the audience will perceive him a certain way, and it doesn’t take much to portray one character as “out of place” to the rest of the settings.

Here’s Christopher Walken taking about it. He plays a great villain, and has a lot of interesting things to say. But cut to 3:20 if you want to go straight there.
http://www.youtube.com/user/HuckleberrySlim?feature=mhw4#p/f/11/poy67cTeQuw

I think the main signs are rather subtle, and have more to do with affect than some extreme expression. Flatness of expression, dullness of response, the beginnings of tardive dyskinesia, all these suggest a person under the influence of large doses of neuroleptics – in other words someone who is psychotic.

I would imagine that it would look a little like Dick Cheney after he’s just eaten a live puppy.

Nervous knee jiggling. Barely visbly shaking fingers. Dark, unexcited look on face, as if expecting nothing good can happen.

If speaking, depending on illness and phase of illness—sometimes a slow, drawling, flat voice with little or no expression, or an aggressive, slightly belligerent tone of voice with also a tinge of anxiety—sometimes fear. That’s bipolar.

Schizophrenics, if medicated, can look pretty normal, but they might seem slightly less aware of their impact on others.

The other illnesses will be different.

If you want a stereotype, I’d add an inability to make eye contact. Rapid speech. Sometimes slurred. Incomprehensibility.

Jack Nicholson comes to mind…

I just typed about 30 lines describing my lunatic then I accidently deleted it….ggaaarrrrkkk! I will get back to starting it again tomorrow. Great question.

There should be some rocking going on, definitely rocking.

I’d like to point out that the terms “insane” and “insanity” are legal terms. They’re not terms used in a professional mental health setting.

Also, I must agree with @Cloverfield , most people with mental illness do not give visible signs of being mentally ill to an untrained eye.

Perhaps what you’re thinking of are the ticks left over from inappropriate medicine?

Act drunk.

Some people are very adept at hiding insanity from the world, therefore insanity lurks in plain sight and in greater numbers than people would think.

For particulars to acting some research is in order. Look up the symptoms of paranoid schizophrenia, obsession disorders, and any others you can think of.