A-Rank: "Capture a Control Point!": Team Fortress 2 reference. When you succeed, "You get an ubercharge and fire your minigun maniacally, yelling 'CRY SOME MORE!'". If you lose, "you charge in recklessly and get mowed down by a sentry gun."
A-Rank: "Defeat the Army of Darkness": from the movie of the same name. The win message reads "You grab your chainsaw and hack through the walking dead. Groovy!"
A-Rank: "Diagnose a Patient!": "After messing up four times, you do a lumbar puncture and find out it's actually lupus!" Mess up, and "you get stumped and some snarky guy with a cane fires you."
Wasteland: "Hunt the Rubber Pirates": Reference to Luffy from One Piece.
"Karate Yes": Replicates the basic training given to Daniel in The Karate Kid. Basically, MC Stripeypants (Urahara) wants you to Wax Off and wash his car.
"2 B A Master": Named for the first English-language Pokémon theme song. The quest text even reads "You want to be the very best...LIKE NO ONE EVER WAS".
"Wish Around the World": A reference to the ending them to the Spice and Wolf anime's first season.
"St. Flash's Day" and "The Freshest Move I've Ever Seen": Both these quests and their rewards (the Running Man jutsu and the "Floating on Air" theme) are references to the video for "Something Good '08" by Utah Saints.
The Paper (Konan) looks like and is named for the codename used by Yomiko Readman of Read or Die.
When you complete the steps required to get Anonymous (L) to join your party, he cries "We cannot forgive! We cannot forget!", the motto of the internet collective (or not) of the same name.
Tsukasa is a double-reference. She starts out as the Tsukasa from Lucky Star (along with Lucky Star-themed allies Kagamin, Kona-chan and Yuki-channote the latter two are Tsukasa's nicknames for Konata and Miyuki, respectively), but after she levels up, she takes on the appearance of a different Tsukasa...the one from .hack//SIGN.
Speaking of Tsukasa, pairing her up with Yuki-Chan earns you the "Moe Points bonus", a reference to a speech given to Miyuki by Konata about her clumsiness being seen as cute to others.
With the release of Perfect Poker (itself a shout-out to Gamble Fish), a new set of allies have become available. The first one, Potatoes, is basically Sasha from Attack on Titan.
Most of the jutsus taught by the characters are named directly after the ones that are used by their Naruto counterparts. Of those that aren't:
When she gets promoted to level 3, Pinky (Sakura) is capable of teaching a jutsu called "This Fist of Mine" (a play on Domon Kasshu's "This hand of mine..." battle cry in Mobile Fighter G Gundam). note Amusingly, BvS actually has a Domon-like character in "Doughman", and you can learn "This Hand of Mine" from him, but it has a different effect than Pinky's "This Fist..."
Summoning and defeating a WorldKai gives you the trophy "Dai Sei Kou!"
If you and your village are able to survive on a Zombja map for 28 days, or defeat all of the Zettas and seal off the gate, you will receive a trophy called "28 Dayrolls Later".
Those who have "Survived the Impossible" get the option to "Be a Hero", giving you a single action protected against the cruelty of the Random Number God for that map. In doing so, you get a message that says "Rule 17 Broken", a nod to Zombielandnote Columbus' Rule #17: Don't Be a Hero.
For maxing out any of the Z-Skills, you earn the trophy "It's a Trick".
The H.A.R.O. explosive device is a reference to the F.L.E.I.J.A. from Code Geass
At the "Juice" Bar, there are a bunch of different drinks named after BvS characters and elements. One of the listed drinks is Rum, but the input box is disabled, and the flavor text next to it reads: "Where has the rum gone?"