The alias of the secretive John Reese is an homage to Batman's The Riddler (i.e. E. Nigma is made to sound like enigma) as Mr. Reese is made to sound like "mysteries". This type of sound bite was used much earlier in a TV show. In the 1960's British TV show, The Avengers (1961), the female lead, played by 'Diana Rigg', was named "Emma Peel" to sound like "M (or Male) Appeal ".
The character of Sameen Shaw was introduced on the show with the potential of becoming a regular, but it only happened because she was well received by the audience and the producers were happy with Sarah Shahi's performance.
Showrunner Jonathan Nolan said the writing team decided to make Root a prominent character mainly because of the theme music composer Ramin Djawadi wrote for her. In an interview, he once said "Ramin had written this theme for Root and it was amazing. It's a really fun, mysterious character, but we really wanted to hear that theme again! So when we came back to the [Season 1] finale again, we know where we wanted to go with the character".
The character of Carl Elias shares similar traits with Professor Moriarty, the nemesis of Sherlock Holmes; both men masquerade as kindly school teachers whilst secretly commanding a criminal empire in the shadows. Both are consistently at odds with a pair of mystery-solving enemies, Holmes and Watson, Finch and Reese. Both have right hand men with the surname 'Moran'.
Finch generally uses fairly identifiable bird-based or bird related aliases with the first name Harold (Harold Wren, Crane, Crow, Quail, Gull, Swift Starling, and Mr. Partridge) but has used non-bird names including Arthur Bellenger, Thomas Paine, Dr. Tillman, Lucas Bennett, and Walt Trowbridge. The alias Norman Burdett could be considered bird-based (bird-ett). In Season 2, during John's interrogation, Finch's alias is "Howard French", which is not a bird name, although based on Reese's former profession and the likelihood of capture and torture, choosing phonetically similar aliases can be very helpful should the need to use them arise. In season 3, episode 21, "Beta," the grave site his fiancé visits has a name plate with the name Harold Martin. At first glance, this would not seem to be a bird related name, but it actually is. There are many species of Martin around the world, including a very common bird in North America, the Purple Martin, and another from South and Central America, the Gray-breasted Martin, and many others.
All of Reese's aliases have the first name John (John Reese, John Rooney, John Warren, John Anderson, John Wiley, John Campbell, John Randall, and John Hayes) except for his first alias in the pilot (James J. Manzione) and Mission Creep (Tony Miller). He also goes by "Detective Stills" and "Marshall Jennings", having "borrowed" their shield/star somewhat permanently. However, these aliases are usually only used when necessary to gain access to an area or information that would otherwise be much more difficult if not impossible.
Showrunner Jonathan Nolan stated that he knew Ramin Djawadi, the composer of the show, ever since he worked with him on his brother, Christopher Nolan's Batman Begins (2005), where Ramin did additional music for Hans Zimmer. Nolan described Ramin as "unbelievably talented", and he said that sometimes when they decided to use a song in the show, Ramin would come with an original piece he composed and Jonah had to say "Sorry, Ramin's s**t wins again!". Later Jonathan chose Djawadi as the composer of his HBO project, Westworld (2016).
During seasons 3 and 4, writers noticed the chemistry and enjoyment on screen between Sarah Shahi and Amy Acker, so decided to develop the Shaw/Root romantic dynamic by writing them more scenes together and playing with their sexual tension.
Bar episode 6, which scored an 8.9, the final season has the rare distinction of having every episode rated above 9 by user reviews, with the season and series finale having the even greater distinction of earning a perfect 10.0.
In Person of Interest: Mission Creep (2011), when the camera pans through items in the police evidence locker, a large Virgin Mary statue can briefly be seen, similar to the miniature ones filled with heroin in the TV show Lost (2004), another show executive produced by J.J. Abrams.
It is mentioned throughout the series that Mr. Reese was a former military Special Forces operative (Army Rangers, Delta Force then Green Beret) who then became a CIA Operative before coming to work with Mr. Finch.
The trivia items below may give away important plot points.
In surveillance camera shots from The Machine's perspective, The Machine assigns color-coded boxes to individuals it is monitoring at that time. White boxes are default and the most common, while white boxes with red corners identify (irrelevant) perpetrators. Individuals knowing about The Machine get yellow, threats to the system red boxes. Later, the show introduces blue boxes for agents of Primary Operations (relevant numbers) and a black box with yellow corners for its Analog Interface.
It was in between the show's second and third seasons that Edward Snowden came forward with details on PRISM, a government program designed to spy on U.S. citizens in order to detect terrorist threats, which is very similar to the show's fictional "Machine" and how it operates. This similarity is later referenced in Person of Interest: Lethe (2013), where, at the end of the episode, PRISM is listed as a decoy of The Machine.
Several nods are made to The Count of Monte Cristo throughout the show. The book shows up as a school assignment in Person of Interest: Witness (2011). The teacher who assigned that book, Elias, has a back story similar to that of Edmond Dantes. In that he was betrayed by someone close, put in prison, presumed dead. Later freed, ready to dish revenge to all back stabbers, and take over the world he previously was just grateful to be a part of. Dagmara Dominczyk who played a POI in Person of Interest: Many Happy Returns (2012) also played the fiance of Edmond Dantes in The Count of Monte Cristo (2002).