The "Gentlepoints" Secret Archive file describes an organization in the United Kingdom that keeps track of how many "gentlepoint" a gentleman has based on the formula, "(Old ladies escorted across the street) x (tophats owned) x (puzzles solved) x (money given to gentleman-tracking organization)". This is a reference to Professor Layton. The series is set primarily in England, with the titular Professor Layton being a self-identified gentleman and puzzle-solving detective, who wears a tophat.
When Sigma accuses Dio of planting the bombs, he points towards him with his index finger, while stating "Was you! Dio!". Just afterwards, when Dio states that Sigma is going about things backwards, the latter retorts with, "So? This isn't a court". This is likely intended as a reference to the Ace Attorney franchise. Sigma also happens to be wearing blue, the same color as Ace Attorney's Phoenix Wright.
When searching the Control Room, examining the cardboard boxes while on easy mode will prompt Phi to wonder if they could be used to sneak past guards. This is a reference to the Metal Gear franchise, in which Solid Snake can often times use cardboard boxes to move stealthy past enemy guards.
When he was a child, Kyle apparently liked to play the puzzle mobile game, Angry Birds.
Live Action Television
In the Crew Quarters Sigma uses the internal phone line to call Phi. When calling her for a second time, she'll answer the phone by saying, "Welcome to Good Burger, home of the Good Burger". This is a catchphrase from "Good Burger", a sketch on the American comedy-variety show All That, which gained it's own 1997 movie.
Several references are made to the British sci-fi show Doctor Who.
Betty in the manufacturing room makes several references, stating "I'm the Doctor! Who? WHO! HaHa Time!" as well as "Wibbly-wobbly timey-wimey". The former is a reference to both the show's title and the titular protagonist "The Doctor". The latter is a reference to a popular quote from the episode "Blink" when the The Doctor is attempting to describe the concept of time.
The name of the trophy for activating the Force Quit Box , "Bigger on the Inside", is a reference to the TARDIS . The TARDIS is a machine with a vastly bigger interior compared to it's exterior, that can travel through time and space. This fits in with the Force Quit Box, as when it is activated it causes the players to decide to SHIFT through space-time.
In the laboratory, examining the beakers several times eventually prompts Sigma to go, "meep meep meep". This is in reference to the character Beaker from The Muppet Show, who speaks in a high pitched sound often spelled as "meep" in official books and merchandise".
The secret archive file called "The Secret of Quark's Hat" proposes the notion that Quark could be hiding "Ferengi ears" under his hat. The Ferenji are a extraterrestrial race from Star Trek, the members of which have exceedingly large ears. Specifically, it is likely a reference to the Ferenji from the Deep Space Nine spin-off series who shares Quark's name.
When she introduces herself to Sigma, Phi lists words relating to "man" before stating "I guess you could say, I am no man". She then says, "One of these days, Witch-king..." This is all in reference to The Lord of the Rings film series, which is based around a novel of the same name. Specifically the character Éowyn, who in The Return of the King disguises herself as a man. She confronts the Witch-king of Angmar, who boasts that prophecy dictates that no man will ever be able to kill him. Éowyn declares that she is "no man", and ends up striking the killing blow to the Witch-king.
During her "I am no man" speech, Phi lists "wolfman" as one of the "man" examples she claims not to be. This could be a reference to movie monster, that first appeared in the 1941 movie, The Wolf Man. Incidentally, the 2010 remake contracts the name into one word akin to how it is said by Phi.
The trophy/achievement for opening the tenth lock in Virtue's Last Reward and locating Dio's Number Zero bomb is "Some Days You Just Can't Get Rid of a Bomb". This is a reference to a particularly infamous scene in the 1966 film Batman: The Movie. In the scene, Batman runs around with a comedic looking bomb. In every place he tries disposing of it there are innocent pedestrians, or ducks, prompting him to eventually state in frustration, "some days you just can't get rid of a bomb!"
The "The Secret of Quark's Hat" file suggests that Quark might be a "young Lobot" due to his bizarre hat. Lobot is a character from the Star Wars franchise, who has a cybernetic device attached to his head.
When they are searching the Kitchen, Junpei sarcastically retorts to Lotus with, "Well excuuuuuse me, princess." This is a reference to the The Legend of Zelda TV cartoon series, which is based on the popular video game franchise of the same name, which in the protagonist Link would often exclaim "Well excuuuuuuse me, princess" towards the titular Princess Zelda.
In the Lounge, examining the the Planet Liquor prompts Phi to drool while stating, "with our powers combined..." This is in reference to the 90s cartoon Captain Planet and the Planeteers. In the show, the five teenage "Planeteers" could combine their powers to summon Captain Planet, often accompanied with a variation on "with our powers combined".
Anime & Manga
Upon examining the billiard balls poster in the Rec Room, Alice humorously wonders if they are "those balls from that kid's show", which grant a wish when seven of them are gathered. This a reference to the Japanese anime and manga franchise Dragon Ball, which follows Son Goku as he attempts to the Seven Dragon Ball orbs, which are said to summon a wish-granting dragon when gathered together.
During her "I am no man" speech, Phi lists a number of Comic Book superheroes:
Dialing 5309 on the phone in the Crew Quarters connects you to someone called "Jenny". Sigma says that he "saw [her] number on the wall--" before being hung up on. This is a reference to the 1981 song 867-5309/Jenny, which is about a girl called Jenny who's phone number, "867-5309", is written on a bathroom wall.
The "Floor A and Floor B" secret file jokingly mentions a rumor that "A" and "B" are actually a reference to a "particular Swedish pop-rock group from the seventies". This is referring to the Swedish pop group ABBA.
The HELP archive, "The More You Know, part 3", in Virtue's Last Reward, states that the History button can be used to "rewind dialogue, so you can check before you wreck". This is likely taken from the saying "check yourself before you wreck yourself". Although the saying dates back to decades prior, it gained popularly in popular culture thanks to the 1993 song Check Yo Self by Ice Cube which contains the lyrics, "check yo self before you wreck yo self".
The Trophy in Zero Escape: The Nonary Games for seeing 999's submarine ending, "We All Die By a Yellow Submarine", is a reference to the 1966 Beatles song, Yellow Submarine, and it's lyrics, "well all live in a yellow submarine".
After explaining the rules of the Nonary Game: Ambidex Edition, Zero III tricks the participants into thinking he is going to cry over having to never see them again. When Sigma becomes irate over this, Zero III replies with, "You mad?". This is a phrase that is associated with the online act of trolling, where someone attempts to spark an emotional response in someone by purposefully creating discord.
The trophies/achievements for opening the seventh and ninth locks in Virtue's Last Reward are called "Who Set Up Us The Bomb, Part 1" and "Who Set ero Wing is notorious for it's broken English translation, with the line [ 何者かによって、爆発物が仕掛けられたようです ] being translated as "Somebody set up us the bomb".
The "EU" secret file give how "Erotic Units" certain American icons would rate.
20/20, Marilyn Monroe - an actress and model who was a sex icon of the 50s.
16/20, Danny Trejo - actor who's starred in numerous hollywood films.
The trophy/achievement, "I Can't Believe It's Not Murder!", gotten by opening the second lock in Virtue's Last Reward, is a reference to the margarine butter-substitute brand, I Can't Believe It's Not Butter!.
In the Crew Quarters, upon phoning Phi, she'll mistakenly read "asterisk - asterisk - 9 - 2" as "agricola - agricola - 9 - 2". Sigma responds with, "I didn't know you were into German-style board game farming simulations". This is a reference to the euro-style worker placement board game Agricola.