Back in 2011....the CBS folks came out with an unusual story-line and show....Person of Interest. It took around four episodes to convince me of a decent program, and by the middle of the second year....I had interest in watching each episode. Last year, after 4.5 years and 105 episodes....it ended.
There are probably ten shows that I put into the category of 'under-weight' and and deserve a re-boot....a totally different version of the original series. I didn't really think in this manner much about re-boots....until I saw Battlestar Galactia (version 2). In certain cases....re-boots make the the story-line better, and I think Person of Interest is one of those shows.
How I would change it?
1. Dump the name. It was a lousy choice. It should have been "Man in a Suit" and every episode should have had some witness describing the John Reese-character as a man in a suit.
2. As geeky as they tried to make the Finch-character....I think it was only 75-percent of what the real Finch should have been.
3. Somewhere along the 10th episode, Finch should have had this moment of reality hit him that system (which he'd been working on for six years)....had already broken off with the AI (artificial intelligence) stuff, and created it's own logo, brand-name, company, and was hiring people for various agendas. Finch should have spent a dozen episodes in a shocker state over his system taking off without him and virtually uncontrolled.
4. At some point in the second season, I would have John Reese confronted with impossible odds and needing mostly a miracle to occur, when the system tells Finch that it's called on the 'Spartans'. Within minutes, a dozen characters appear out of thin air and rescue Reese. Finch would quietly ask the system....who precisely are these folks? The system would respond that they are the B-team....people that just needed focus in life. The system would refuse to discuss the team or the ultimate purpose.
Oh, I think the original show did a decent job. It's just that it could have been better.