Like the movie, every episode opens with a (false) declaration that it's based on a true story with the names changed.
The opening shots of "The Crocodile's Dilemma" and "Eating the Blame" are similar to the opening shot of the movie.
With his weird haircut and stoical sadism, Lorne Malvo brings to mind Anton Chigurh of No Country for Old Men. Malvo even gets a scene of performing surgery on his own leg, like Chigurh.
Throughout "The Crocodile's Dilemna," Lester Nygaard seems like a copy/paste of Jerry Lundegaard, until he kills his wife, at which point he starts becoming something else entirely.
Molly Solverson is loosely based on Marge Gunderson. This is more evident after the Time Skip, when she's a more confident detective and heavily pregnant. She also has a conversation in bed with her husband who is falling asleep while watching television about how they're "doing good." Marge does the same thing in an early scene of the film.
The restaurant where Lester meets Malvo is advertising white Russians, the Dude's signature cocktail in The Big Lebowski.
Malvo's collection of recordings of people he's corrupted includes tapes labeled "Carson Wells" and "Everett McGill."
While passing a janitor mopping the floor, Malvo tells him, "You missed a spot." This is a reference to the opening montage of Raising Arizona, when H.I. passes the prison janitor mopping the floor and tells him the same thing.
Lester tries to get some "unguent" for his hand infection in "The Rooster Prince." In Fargo, Grimsrud declares that he needs "unguent" for his hand wound when kidnapping Mrs. Lundegaard.
When Lester pulls Don Chumph the personal trainer into a closet, a box is labeled "Misc. Labeouf," referencing the character Labeouf in True Grit.
Malvo kidnaps a man from McDonnough & Snoats Accounting and Consulting. The name is a reference to protagonist H.I. McDonnough and his former prison pals the Snoats brothers in Raising Arizona.
As a dimwitted personal trainer who greatly overestimates his skill at extortion, Don Chumph is an Expy of Chad Feldheimer from Burn After Reading.
One of the Bemidji deputies is named Knudsen, the original surname of Bunny Lebowski in The Big Lebowski.
The opening shot of a simple prairie field paired with Appalachian folk music in "The Six Ungraspables" is evocative of O Brother, Where Art Thou?.
Molly's awkward and plot-irrelevant dinner with a former school friend is a reference to Marge's similar dinner with Mike Yanagita in Fargo.
The anecdote about the rich man who gave away everything to the poor, including his own life, is reminiscent of the pointless "Goy's Teeth" sequence in a A Serious Man, except for being considerably less pointless.
In "Who Shaves the Barber," Bill mentions that six Bemidji residents died in a pharmacy fire in 1978. Anton Chigurh blows up a car outside of a pharmacy in No Country for Old Men.
Stavros enters a garage, immediately tries to drive out again, and gets into an argument with the attendant over whether he has to pay, just like Carl does in Fargo, only Stavros convinces the guy to let him leave.
Lorne has a conversation with a man that will determine whether the man will live or die. We then cut to Lorne grimly exiting the front door without learning whether he killed him. This mirrors Anton Chigurh's confrontation with Carla Jean Moss in No Country for Old Men.
The Fargo Mob's headquarters is located in the Showalter Block. Showalter is the surname of Carl, the "funny looking" kidnapper in Fargo.
At one point, Lou is switching channels and passes the "bark beetle" documentary watched by Mrs. Lundegaard.
Molly's conversation with a hospitalized Mr. Wrench is very similar to Marge Gunderson's words to Gaear Grimsrud.
The portrait of two bikini-clad women on the beach is an allusion to Barton Fink.
The fact that Malvo temporarily becomes a dentist is a nod to A Serious Man.
A major plot-relevant one. Molly's and Gus's marriage follows cues from Marge's and Norm's marriage.
In "A Fox, A Rabbit, and a Cabbage," Stephen Root's character calls Lorne "friendo", another allusion to No Country for Old Men.
In "Morton's Fork," the camera lingers on a car's dealer plate, which is even marked "DLR."
The season ends with Gus, Molly, and Greta sitting together on the couch, watching television as a family, mirroring the final scene of the original film. Additionally, both stories end with the female protagonist pregnant and still slightly perturbed by the events she's had to deal with.
The confrontation between Malvo and Lou in Lou's diner plays like a foil to the famous scene in No Country for Old Men where Chigurh takes offence at an innocent comment from an unwitting gas station owner and proceeds to gamble for the man's life over a coin toss without the other man being fully aware of what's happening. Except in this series, while initially Malvo clearly thinks he's dealing with a hapless rube as Chigurh was, to his discomfort it turns out that Lou is a lot more savvy to the type of person he is and isn't easily intimidated.
Others
The hallway and elevator in the Las Vegas hotel where Lester encounters Malvo again resemble those in The Shining.
Mr. Wrench and Mr. Numbers are dressed like Joe Buck and Ratzo Rizzo from the non-Coen Brothers film Midnight Cowboy.
When Malvo walks into the dinner he orders coffee and is offered [[cherry pie]].
Similarly, when Molly and Bill interview Lester following his wife's murder, the topic of conversation briefly drifts to a chewing gum he liked...
After Malvo kills Mr. Numbers, he frees Mr. Wrench from the hospital and tells him "if you still feel raw about it" to come see him. This mirrors the Bride's words to Nikki in Kill Bill after the Bride kills her mother.
