Moore's Law suggests, at its most basic, that computer processors double in complexity every two years. Such is the case with Person of Interest, which has doubled down on its intrigue to hastily evolve from a bland procedural with a nifty visual aesthetic (important information is relayed through various surveillance devices) into a solid action-thriller that intersperses twist-filled standalone episodes into its season-long arcs.
The show's been able to develop its relatively taciturn protagonists via flashbacks. We've seen the fallout that led John Reese (Jim Caviezel) to part ways with the CIA; he's now more than just "the man in the suit," though he's still generically and almost jokingly described that way. Likewise, his billionaire backer, Harold Finch (Michael Emerson), no longer seems so distant and eccentric, now that we've seen his paranoia borne out, and various kidnappings (and the company of a loveable attack dog) have gotten him out of his self-enforced seclusion. Even the unseen Machine that doles out each week's "person of interest" like a mechanical Charles Townsend has gotten a backstory that stresses its autonomy and almost frightening ability to evolve. Folding characters like NYPD detectives Carter (Taraji P. Henson) and Fusco (Kevin Chapman) into the main plot has also paid off, as it's far more compelling to see these two attempt to help Reese than it was to see them attempt to bring him in for vigilantism.
In short, these persons are now actually of interest, enough that the joy of hanging out with them for another week is sometimes enough to coast through some of the more clichéd or over-plotted episodes. Better defining these roles has also helped the writers grow confident enough to promote two recurring characters to full-time members. Samantha Shaw (Sarah Shahi) is the unpredictable and much-needed rogue, a hot-blooded ex-assassin who isn't nearly as bottled up as Reese; likewise, Root (Amy Acker), provides a neat counterpoint to Finch, for while she matches his pure logic and cold calculations, she also has faith in the Machine, which she communes with and likens to God. These two add much needed perspectives to the third season, from Shaw's ruthless version of levity to Root's psychopathically developed techno-religion.
The only thing that hasn't evolved on Person of Interest is the regular casework. Given how many cop dramas there are, it can be hard to come up with interesting, new crimes, especially when trying to surprise audiences with a twist—even if the gimmick is that Reese is attempting to stop the crimes, whatever they might be, from happening. But this means that some episodes, like "Reasonable Doubt," don't make it beyond the initial premise of the series: the Machine gives Reese and Finch a new "person," but doesn't tell them if that person's the victim or the perpetrator. In 20 minutes, the episode's person of interest, Vanessa Watkins (Kathleen Rose Perkins), pulls a Fugitive to prove she didn't murder her husband, tricks Reese with an unassuming Usual Suspects bit, and is revealed to actually be executing a Double Jeopardy: Her husband isn't actually dead, but she's damn well going to kill him now! It's all a bit silly and exhausting, especially if you're familiar with the underlying tropes: You have to be as playful as Castle, whose main character—a writer—is always commenting on the plausibility of the story, to get away with that.
Far better are episodes like "Lady Killer," which both play against expectations and give the characters a personal connection. In this case, Carter, Shaw, and Reese's love interest, Zoe (Paige Turco), are all out of their element when they go clubbing in the hopes that they can bait a suspected serial stalker/killer (Warren Kole) into making a move on them. (They're much more comfortable, if not outright giddy, when it comes to comparing their concealed weapons.) The season premiere, "Liberty," doesn't even bother committing to its central plot, skirting over a Navy smuggling operation so it can spend more time hanging out with the characters: a flustered Fusco, fussing with a bomb; Reese, introducing Finch to his first boilermaker as nonchalantly as he strolls into the middle of a Mexican standoff ("I'm sorry, are you closed?"); or Shaw, less bothered by the corpses strewn at her feet than by her constant hunger ("You're buying me a steak," she informs Reese).
Person of Interest is at its best when sticking to cutting-edge topics, be it Root's philosophical extremes or ethical discussions of surveillance (as in "Nothing to Hide," which introduces a group of privacy-seeking terrorists), and in demonstrating the limitations between what the Machine can accomplish on its own (hacking just about anything) and what only someone like Shaw can manage (infiltrating a trophy wife's boozy bookclub). The exponential extent to which the series can truly evolve, then, depends on how willing and able it is to shed some of the older plotlines and characters, specifically those dealing with the tired issue of police corruption. After all, as the computers of Moore's law demonstrate, more can certainly come from less.