In an early episode, Maria Dizzia's character Polly includes the secret ingredient of blueberries in her soap, which is one of the things that makes Piper so excited about going into business. This may be a subtle allusion to Dizzia's character Dolores on Louie, who has a penchant for blueberries.
Alex and Piper are called into Healy's office after Pennsatucky trapped Alex in the laundry dryer; Healy's only concern is whether they've been using the dryer for lascivious purposes. Alex responds, "I'm more of a dishwasher kind of gal, sir." This is an allusion to Donna Pinciotti, the character Laura Prepon played on That '70s Show, who mentioned being aroused by dishwashers.
Between him referring to the "webcam incident" and the "penis-shaving horror" in the first episode and the scene with him attempting to "edge," the show doesn't shy away from references to Jason Biggs' breakout role in American Pie.
Nicky refers to Gina as "Squirrel." This could be a reference to Abigail Savage's role as Bunny.
Dawson Casting: Subverted. The inmate actresses play their characters well into their late-teens for flashbacks, but their ages are not revealed.
Fake American: Brooklyn-Italian Lorna Morello is played by Australian Yael Stone.
Fake Russian: Galina "Red" Reznikov is played by the Irish-American Kate Mulgrew
Genius Bonus: Morello mistakes the name of Bora Bora for "Bora Bora Bora." She's apparently confusing the country's name with "Tora Tora Tora," the Japanese codeword announcing the successful sneak attack of Pearl Harbor, which served as the namesake of the war film Tora! Tora! Tora!