"Jump the shark", if you don't know, is when something happens that causes you to realize things are never going to be as good as they used to. The opposite would be when be when something happens on a series that makes the series dramatically better.
When Michael Emerson joined Lost, it crystalized and clarified the drama, he gave the show something it needed. At that point, Lost stopped being a rambling drama that didn't seem to be going anywhere. Suddenly, the "Others" stopped being strange weirdos and started being interesting. The "Others" even started dressing better.
In the seventh episode of Fringe, they introduced David Robert Jones (played by Jared Harris). Up until this point, they were vague about something called "The Pattern". It really felt as if the writers didn't have any more idea what was happening then the viewers. The enemy had a face. The writers weren't wandering aimlessly from incident to incident, they had a focal point, a direction. The episodes became markedly better written. The characters were actually striving for something.
The reason that I'm bringing all this up is this- I've just watched the first season of "Lie to me" and I really like the show, but I really think that they need to have a Michael Emerson or David Robert Jones. I really like "Lie to me", but Tim Roth's Dr. Cal Lightman hasn't really found a match- the Joker to his Batman. Somebody to battle through the show's future seasons. I just hope that they don't do a "House" like thing and make his enemy a bureaucrat that battles over petty crud- "Fringe" tried that with Michael Gaston's Sanford Harris and it was utter crap. Nobody ever wants the enemy to be red tape or bureaucracy - unless it's a comedy.