There's a unique enemy that has a chance of spawning somewhere in Magnys Lighthouse. His name is Mr. Bubbles, and he is accompanied by a midget named Lil' Sis. If you kill Mr. Bubbles without harming Lil' Sis, she will stop being hostile and give you a gun called Little Evie.
The Mysterious Amulet of the Tiny Tina DLC is a reference to the Pendant in Dark Souls. Specifically, as an item of unknown benefit that might possibly be put in the game simply just to confuse players and cause them to speculate.
Incendiary Bandit weapons are tagged as Fire Fire weapons, appropriately enough for weapons made by dumb, childish pyromaniacs.
Too Close For Missiles: questgiver "Loggins" tells you to go to the "Goose's Nest" and deal with a shirtless men wearing aviator glasses who play volleyball. The completion screen is also a direct parody of the movie's opening crawl.
After dropping the pizza: "Hey, you're not June! GET 'EM, DUDES!"
"No Vacancy" references Gearbox's expansion to Half-Life, Opposing Force, where you need to find a valve and a gearbox to proceed. Here, you need to find a steamvalve and a gearbox. Sadly, no giant alien worm.
Won't Get Fooled Again: Where you need to find the culprit in a crime. If you get it right, the quest even ends with a one-liner worthy of Horatio Caine himself.
A Real Boy: A robot wants to become human, and as a reward he gives you a gun called Fibber, which lies about its own stats (but is still a good gun due to having a number of unique effects, some of which are significantly more powerful than others.)
Assassinate the Assassins: The bonus objective for the fourth assassin asks that you MDK (Murder Death Kill) him with a shotgun.
For part of Animal Rescue, the text when you start each part are a reference to If You Give a Mouse a Cookie, e.g. "If you give a skag some medicine, it's going to want some food...".
The Bagman in the Clan War questline is referred to as a leprechaun, and when you ambush him, he says "They're after me money!", a clear reference to the Lucky Charms mascot. The initial description of the quest ("Hearts, stars and horseshoes...") is lifted from the cereal's longtime jingle.
Tiny Tina's Assault on Dragon Keep is filled with shout outs and references to MMOs, nerd culture, and other things.
When you first see her, she greets you with "O hai!"
One quest is nothing but a giant reference to Dark Souls with the Vault Hunter helping out what is, by all appearances, a Dark Souls player down on his luck. There's a part where you fight giant skeletons in a graveyard, the stuff you grab for him comes with the item description "You sense agony. Despair. Snapped controllers," and at the end of the quest, the game is 'invaded' by a huge, red-tinted knight who uses recognizable moves from the game. The player advises you at the end to "Hold on to your humanity."
One quest has you being sent after Prince Jeffery, who sits upon an Iron Throne made up of guns and has guards named Molehill and Canine (a reference to Gregor and Sandor Clegane, who are known as The Mountain and The Hound respectively). The main joke of the quest is that Mordecai doesn't get the references since he doesn't watch Game of Thrones, instead watching a show about duchesses getting married.
The mission My Dead Brother has the rather simple description of "Bro team kill."
The mission Fake Geek Guy features Tiny Tina asking Mister Torgue various nerd culture related questions to test if he is a real nerd. These include references to Star Trek (the frequent deaths of Red Shirts specifically), Lord of the Rings, and Doctor Who.
According to writer Anthony Burch (on one of his Twitch TV Livestreams), Handsome Jack's name is a reference to Captain Jack Harkness, who is referred to as "Handsome Jack" in the Tenth Doctor episode "The Sound of Drums". Originally it was just a placeholder name, and Anthony asked, "You're not going to ship it with him still named that, are you?" They did.
Loggins in The Dust spouts a lot of Top Gun References. "Goose! GOOOOOSE! I'm in the danger zone man!", "I'm Requesting A Flyby" and so on. His associated mission is crammed to the brim with references to the film (and its astonishing amount of homo-eroticism).
The sliding elevator up the the Varkid Ramparts is a homage to AKIRA. There are several similar elevators in other locations as well - one at the end of the Fridge, and one leading up to the spectator area of the Bandit Arena of Slaughter.
Mister Torgue at one point tells the player that it's "Straight up Dawg Time", a reference to the game "Dudebro: My Shit Is Fucked Up So I Got to Shoot/Slice You II: It's Straight-Up Dawg Time", a game made by the NeoGAF community which, much like the DLC, satirizes Testosterone Poisoning.
Claptrap/Jack: Double Rainbow! Achievement: What does it mean?
One of Zed's radio ads has a warning with numerous shout outs cutting in.
"Come on down to- *WARNING: DOCTOR ZED IS NOT A REAL DOCTOR. HIS USE OF THE WORD DOCTOR IS PURELY FOR STYLISTIC AND AESTHETIC PURPOSES. SEE ALSO: PEPPER, DRE, OCTOPUS. PLEASE SEEK OUT AN ACTUAL LICENSED PHYSICIAN* - Doctor Zed's!"