Real Life example. Jim Caveizel, Reese's actor has many friends amongst the Navy SEAL veteran community who help him train for the projects he works on like POI. Reese's Weapon of Choice, the SIG-Sauer P-226R which also happens to be the sidearm of the SEALS could be a subtle nod to them.
How does Fusco know who he can safely call for backup when Elias is breaking into the safe-house? Thanks to his work as Reese's inside man in HR, he knows just about everyone who isn't an honest cop in New York, and called somebody who wasn't on that list.
Extremely subtle but Finch becomes panicked when someone he cares about like a POI or John is around a bomb. Later in "God Mode", we discover why Harold's Only Friend Nathan Ingham was killed by a bomb while Finch had his back ruined in the blast. After this trauma, when someone he cares about is around one, Harold immediately drops everything and if possible is willing to die trying to save them from getting blown up like in the case of John during "Dead Reckoning"
John Reese was likely the first number from the Irrelevant list that Finch was able to save. (His number came up prior to the events in New Rochelle, and then he was contemplating suicide when we meet him in the Pilot episode 7 months later.)
Disproven as of 'RAM'
Reese pronounces the Dutch commands he uses with Bear with a heavy German accent. If he was stationed in Germany during his military career, he might have picked up the language there. Then he ends up in Iraq, where he starts working with dogs trained to respond to Dutch commands—and his pronunciation of the Dutch words is colored by his prior experience with German.
The Machine was infected by a virus sent by Decima, but inside that virus was another virus which caused it to protect itself from all attempts to gain control over it. Finch didn't make a virus: he made a vaccine.
Why does Root open fire in the asylum three seconds before Hersh steps into the corridor? The Machine is giving her the ability to detect the position of hostiles which was displayed in "God Mode", as a result, she's able to basically lay down suppressing fire and force Hersh to dive into cover, catching him off guard.
Lionel Fusco's days with Stills and the nascent HR hierarchy gave him the skills needed to figure out how to "mock up" crime scenes to look the way a cop wants it to look, so when Carter needs a faked death, Fusco already has everything needed.
"Endgame" reveals how Carter immediately knew Reese had suffered from PTSD back in the "Pilot" episode. Her husband who was a fellow veteran displayed similar traits as their marriage fell apart.
Root's alias Caroline Turing in "Firewall" probably refers to Alan Turing, Father of Computer Science and Artificial Intelligence.
Finch landing the plane in "4C". Why does he already have controls? Because he probably plays flight simulator games, and he's probably flown virtual jumbo jets, which is why he can make the landing (that, and because he's already a pilot, he knows the basics).
From "4C" as well. Reese is going to Istanbul. Why? Because Alistair Wesley in "Critical" mentioned they'd crossed paths at the market there, and Reese wants to follow up on that.
Why is Arthur able to remember Finch and all the shenanigans they got up to in college so easily when he has trouble remembering anything else in "Lethe" and "Aleitha"? Think back on the school song they sang together in "Lethe": The last three words are always remember MIT.
The ISA replaced Shaw with a new operative, Indigo 6 Alpha, who crosses paths with Reese in "4C". While it was pretty humorous that the operative was extremely similar to Reese, it might actually be a clever cover for the ISA. If Indigo 6 Alpha were to get made or happen to operate in New York, they could plausibly pin any crimes or actions he commits on Reese. Given that the only description most law enforcement agencies familiar with Reese is the "man in the suit", it could be easy to confuse them.
For a while, it seemed odd why Finch was insistent with the Machine on not protecting him. At times, it seemed like it was to make sure it did not deviate from its intended purpose to prevent major catastrophes by prioritizing certain numbers (or to not place an "Irrelevant" number over a "Relevant"). Knowing Finch's past seems to spell out a better reason: he is on the run from the government for hacking ARPANET as a teenager. The Machine already showed that it cares about Finch, to the point of matching him with an ideal woman. If his life was in danger, the AI could deviate and send out an Irrelevant number for the government to save, which might end with him arrested. In addition, it might have been a precaution if someone ever managed to gain full access to the Machine, and used it to track him for whatever reason.
When Reese is tailing Benton near the beginning of "Cura Te Ipsum", Benton carries a woman's briefcase as they walk to work; this same woman is the lady who recounts being raped by an unnamed co-worker at the survivor meeting, and her photo also shows up in the files that Reese downloaded from Benton's computer. The worst part about this is that although we don't know when he raped her, it happened sometime before the events in the episode and so she has to face the man who raped her at work every day. Not only that, but judging from the fact that he offered to carry her briefcase he makes sure that she has to see him.
Finch was on the phone with Donnelly when Stanton crashed into his SUV with a dump truck. He would have heard the crash, but have no idea what happened. Imagine how terrifying that would be.
Is it just me, or was the scene where the fake Agent Fahey is about to kill Finch really creepy in an understated way? He has an almost childlike sense of glee as he says, "Are you... like me?" and then he takes Finch's glasses (in a very real sense, stealing an iconic piece of Finch's identity) and puts them on as he begins telling Finch he will become the new "Finch".
Subsidiary: Imagining an identity thiefnote the "serial killer" part is just a bonus, considering that the "irrelevant" numbers are people who would either be dead anyway or would be thrown in jail. Either is convenient from the perspective of "Fahey" in this episode. being in control of The Machine is too horrible to contemplate.
OTOH, the real horror would likely be for "Fahey", as he has no idea what he would be getting into and how many enemies he just acquired.
Also, he wouldn't be in control of the Machine. The Machine knows who 'Admin' really is, and anybody else claiming to be would be summarily ignored.
Equally creepy is "Fahey" repeating his words over and over to pick up Finch's intonation and really become him.
The fate of Hannah Frey. She was kidnapped and murdered. But you have to wonder exactly why. If he was just a sick killer, or if it was for perverse reasons... Definitely not helped by the fact that he redid the porch two weeks after she disappeared.
"The Crossing": it's unlikely that the plump HR cop survived the night after Shaw threw away the pin and left him holding the live grenade.
It is fairly likely it was just a dud, however. Definitely seems like the kind of thing Shaw would do.
In-universe, Finch tells John he experienced this in "Many Happy Returns": He was originally puzzled why some numbers kept coming up over and over again, and thought it was a glitch... until he realised that these were abused women living with their abusive partners.
Fun fact; there's strong evidence that a lot of abuse (up to half of straight relationship abuse, depending on the source) is F>M, and lesbians, depending on which stats you use, have the highest likelihood of all. So how many more numbers is Harold missing?
In "Booked Solid", Hersh notes in his conversation with the Special Counsel that it took him longer than he thought to escape prison. Given that his original goal going in was to kill the four men in suits (Reese and the three mercenaries), the delay might have been him killing off the other two mercenaries. It might have just been to cover loose ends (if they tried to retaliate over Hersh killing one of the trio in "Prisoner's Dilemma"), or in case Reese was a separate threat coincidentally caught with the "man in the suit".