The title "The Rooster Prince" refers to the parable of the same name. A prince is put under a curse where he believes himself to be a rooster, and sits under the table naked pecking at the floor. The king and queen ask around for someone to help cure their son, when an old man volunteers, saying he knows how to cure him. He too takes his clothes off and sits under the table with the prince, pretending to be a rooster. Eventually the prince befriends his "rooster friend" and the old man shows him how a rooster can do human things such as sit at a table and wear clothes. Eventually, the old man is able to bring back his old human habits one bit at a time, curing him.
As Deputy Solverson (Allison Tolman) and Lester (Martin Freeman) exit the drug store, a parking spot is designated "Parking Reserved for Owner Mike Zoss". This is a reference to Mike Zoss Drugs, a Minnesota pharmacy, and no doubt a nod to the Coen brothers (Joel Coen & Ethan Coen) who spent time there in their youth, and subsequently named their production company Mike Zoss Productions, as well as giving the name to the pharmacy that is robbed in their film No Country for Old Men (2007).
When Lester (Martin Freeman) goes to the chemist to treat his wounded hand, he exits the shop to avoid Molly's (Allison Tolman) questioning while the clerk calls out to him "sir, your unguent!" This is certainly a reference to the original movie, Fargo (1996), when Gaear Grimsrud claims he needs "unguent" after Jean Lundegaard bit his hand.
The names on the audio tapes Lorne Malvo (Billy Bob Thornton) listens to correspond to either real names of people who worked on Fargo (1996) or on previous Coen (Joel Coen & Ethan Coen) films, or belong to the movie industry, or character names (Carson Wells for example).