In Beigoma's report card/character profile, her first name is based on the word "Beigoma", which are Japanese spinning top toys that are traditionally made out of Japanese Babylon shells. The object of the game is to spin two Beigomas in an arena and have them try to topple one another to see which one stops spinning first. Beigomas are actually believed to be the origin of the popular Beyblade toys. This means Beigoma Kiyoshi's first name is an indirect reference to Beyblade.
In Beigoma's report card/character profile, her birthday is April 24th. Her birthday is the same date of the birthday of Kobato, the main character of the manga/anime series called "Kobato". This is because Beigoma Kiyoshi's design, as confirmed in her report card, is inspired by Kobato.
In Soshun's report card/character profile, his birthday is August 18th. His birthday coincides with the release date of the first ever Scott Pilgrim book. Scott Pilgrim is happens to be another famous slacker.
In Connie's report card/character profile, her birthday is October 6th. Her birthday coincides with Mad Hatter's day, due to the 10/6 card in his hat. Furthermore, Connie's hat also has a 10/6 card, just like the Mad Hatter from "Alice in Wonderland".
In Part 3, some characters created references.
Jose Historia makes it clear that he is a fan of "The Adventures of Sherlock Holmes". As he also dresses like Sherlock.
Cam Yano makes a reference to "Superman" by questioning if the anonymous head of the Paradox company was like Lex Luthor.
Connie Takemi nicknames people based on characters from Lewis Carroll's literary works, mainly "Alice in Wonderland" and "Alice through the Looking Glass".
In Part 4, Akira compared the murder of Hajime Hinata to that of the game of "Clue".
Also in Part 4, Nagito compared the fight and chase between Yasuke and Monokuma to the "Tom and Jerry cartoons", as their chase seemed as one sided as theirs'.
In Part 6, Soshun highlighted that the phrase, "Abandon all hope ye who enter here", which was written on the crime scene's chalkboard, was from Dante's Inferno, written above the entrance to hell.
In Part 7, Jose referenced Leo Tolstoy and his book "War and Peace", Charles Dickens and his book "The Great Expectations", Sir Arthur Conan Doyle and his book "The Adventures of Sherlock Holmes", and Melvil Dewey (who invented the method of organizing the books in libraries).
Also in Part 7, one of the files in Hope's Peak Academy's archives talked about the existence of the Seven Kings from the "K Anime". And Monokuma lampshaded the identity of a few of the kings by describing their colors and personalities. Silver King - Yashiro Isane, Red King - Mikoto Suoh, Blue King - Reisei Munakata, and the unknown and chaotic Colorless King.
In Part 8, the Mastermind sang the song "I'll Be There For You" (by The Rembrandts) terribly.
And after that, Beigoma and Akira sang "Never Say Never", which acted as a Call-Back to the Danganronpa: Trigger Happy Havoc anime "Danganronpa: The Animation".
In Part 12, Akira highlighted on how Soshun's transformation into his second personality, the Ultimate Deva, was like the Super Saiyan mode of the main characters in "Dragon Ball Z".
Not only that, but both how Soshun knocks himself out with Hagakure's crystal ball (glass ball) and how he transformed into the Ultimate Deva reminds you a lot of how 'Breakdowns' work in the "Ace Attorney series".
In Part 13, Monokuma claimed to be a better mascot than Mickey Mouse and claimed that Despairadise would become the new most fun place in the world.
In Part 3, though it's just because she's an Ultimate Defense Attorney with experience in court, but she ended up saying a signature phrase from "Ace Attorney", whether she meant to or not.
Another one in Part 3 is when Beigoma questioned if Toko Fukawa was a Magical Girl, due to her ability to change personalities as a result of her DID case.
She then remembers about a different series involving someone transforming via sneezing. Though there was no mention on what that series is, one possible series that fit the description would be "To Love Ru", where a Memorzorian alien can change between a male counterpart named Ren Elsie Jewelria and a female counterpart named Run Elsei Jewelria by sneezing. These two are two different genders with different personalities who have to share the same body.
Also Part 3, Nagito explained that people called Genocide Jill, Genocide Jack, as a reference to the infamous serial killer, Jack the Ripper.
Another reference in Part 3 is when Shiro was about to mention how the game they are playing is similar to the video game, "9 Hours, 9 Persons, 9 Doors". But Junko cut him off because he was about to break the fourth barrier.
Interestingly, it followed up with Aya mentioning how trying to make sense out of Junko's ramblings would be like trying to find the lost city of Atlantis.
In Part 4, during his second attempt in breaking the fourth wall, Nagito mentions that fourth wall breaking is very fun and makes anything interesting. He gives the student's the example of the movie "Deadpool", in which the anti-hero Deadpool was aware of the fourth wall and would constantly break it and talk to the audience.
Also in Part 4, while Beigoma was teaching Connie and everyone else about the concept of "-dere", she told everyone that if they have any concerns or questions about other Otaku terms, they should just Google it.
Another reference in Part 4 is when the killer of the first class trial says that the Despair Anime used to brainwash the world uses the song Tsubasa wo Kudasai, from "Neon Genesis: Evangelion" as background music.
In addition, in Part 4, some of the Extracurricular Course Students made a reference while performing their special move during "Rapid Doubt Annihilation".
From Nate's special move from the Ally Set, "Killer Moves", he appears as a Chibi Nate dress up like an assassin from "Assassin's Creed".
From Yasuke's special move from the Ally Set, "Inception", he questions why it took Leonardo Di Caprio over two hours to do a rebuttal or argument.
Also during the execution of the 1st Class Trial in Part 4, Akira pointed out a few more references:
He pointed out that in "Queen of Despair Junko's Crowning Parade", Kiyotakakuma was dressed up like a hitman from "Golgo 13", an old manga series.
He also described the large seamount overlooking the stormy ocean in "One Woman Army" fits in the painting, "The Great Wave off Kanagawa".
He also pointed out that in "Noh mai! It's time for Junko's Destruction", Hiyokokuma summoned a creature that was like a ripoff version of Godzilla.
And in "It's Alive! It's Alive! ...oh and She's Dead", Akira even pointed out how Nekomarukuma was dressed up as Dr. Frankenstein and Monokuma was dressed up as Igor. The scene itself was a reference to "Frankenstein".
He also pointed out how "Please Insert Coin" was modeled after Tetris.
And finally he lampshaded how "Princess Sonia Gets Her Revenge" is based off of Snow White.
In Part 6, Jonathan commented that Shiro's powerful mindset for puzzles makes him similar to Jigsaw from "Saw". Shiro also compares that game they are forced to play to "Saw" which has games with similar circumstances.
In Part 10, the 21st student described Diablokuma's manner of speech and voice as sounding like a stereotypical American street thug from the fifties mixed with one of the Three Stooges.
In Part 12, Akira told Beigoma that she shouldn't expect their sibling-like relationship to end up like in "Oreimo", where the brother and sister confess their love for each other.
Also in Part 12, when Miaya hacked into one of Monokuma's television screens, she made an opening announcement that is based off of the opening for the old TV show "The Outer Limits", according to Cam.
In Part 13, Halokuma and Diablokuma's introduction is based off the Japanese version of the motto of Team Rocket from "Pokemon", during the earliest season for the Kanto Region.
Also in Part 13, Monokuma summoned four more copies of himself before the five transformed into wearing red, blue, yellow, green, and pink costumes from "Power Rangers". Then they jumped inside the Monobeasts and the large robotic creatures combined and formed King Monobeast Fighter Supreme, much like the Power Ranger's Megazord.