Like the movie, every episode opens with a (false) declaration that it's based on a true story with the names changed.
Rye Gerhardt’s appearance and mannerisms are reminiscent of Carl Showalter.
Otto Gerhardt brings Wade Gustafson to mind.
Skip Sprang's mannerisms, financial troubles and incompetent attempt to partner with criminals are all reminiscent of Jerry Lundegaard.
Ed Blomquist feeding Rye Gerhardt’s leg into a meat grinder references the infamous wood chipper scene.
Ed complains to a storekeeper he's going crazy down by the lake, mirroring a scene from the film.
Peggy's Motive Rant and Lou's calm response as they drive back to civilization when she's under arrest in the final episode is essentially a gender-flipped mirror of the final scene with Marge and Grimsrud. Both involve a decent, moral police officer informing a ruthless murderer of the immorality of their actions in a way that leaves them speechless, but while Peggy initially can't shut up with self-pitying justifications of why all the horrible things she did weren't her fault only to be silenced by Lou's blunt response, in the original film Marge delivers a lengthy monologue to the silent Grimsrud.
The dynamic between Lou, Karl and Sonny mirrors that between the Dude, Walter and Donny in the original film - traumatized veterans sticking together and playing games - though in this case bowling is replaced with bingo.
Karl channels the Dude and sets up an Absurdly Ineffective Barricade to block a door that opens outward in "Rhinoceros."
Covers of "Let's Find Each Other Tonight" from the original film and "Just Dropped In" appear.
The plot of the show following the time-skip borrows a little from Lebowski in following a kidnapping that is more than it seems, in which the hostage and money are never exchanged and the kidnappers follow a counter-cultural philosophy (Nihilism and New Age "Actualisation").
Mike Milligan quotes the Stranger, saying that "Sometimes there's a man..." When interrupted he even bluntly notes "Well, there's a man."
The UFO and rumors of it is a reference to this film.
Like Ed Crane, the protagonist of that film, Ed Blomquist is a simple man in a menial job who loves his wife and tries to do the right thing but ends up losing everything. Unlike that film, Ed's wife is unambiguously a murderer.
Further cementing the connection, both Ed Crane and Peggy Blomquist cut hair for a living.
The shot of a door lock lying on the floor in "The Myth of Sisyphus" is reminiscent of Chigurh knocking the locks out of doors with his cattle gun.
The storekeeper who listens to Ed complain about going crazy by the lake is reference to the shopkeeper menaced by Chigurh.
As Lou chases Hanzee on foot, several scenes evoke the shootout between Llewelyn and Chigurh, including a Good Samaritan driver suddenly being shot in the throat and Hanzee quickly diving behind a parked car, just as Anton does.
In "Morton's Fork," a sheriff's deputy checks in regarding pulling over a pickup for an unsecured load. Sheriff Bell does the same in the film.
Bear marching Simone into the middle of the woods to be executed is lifted from several scenes in the film. The scene is immediately followed with the song "Danny Boy," which features prominently in the film as well.
Miller's Crossing is also the only Coen Brothers film to feature a pair of identical twins, similar to the Kitchen Brothers.
Blood Simple: Dodd getting trapped in place with a knife through the foot is similar to Loren Visser getting stabbed in the hand.
Raising Arizona: In "Palindrome," Betsy has a dream of her family's future that's very evocative of HI's, and uses similar language in the voiceover.
Others:
One of the Gerhardt lieutenants is named 'Roost Bolton' after the infamous sociopath Roose Bolton of A Song of Ice and Fire.
Otto Gerhardt, a terrifying and powerful criminal patriarch incapacitated by a stroke, is likely a reflection of Hector Salamanca of Breaking Bad and Better Call Saul fame.
The Solversons' habit of saying goodnight to each other as, "Goodnight Mr. Solverson. Goodnight Mrs. Solverson, and all the ships at sea," is quoting a catchphrase of broadcaster Walter Winchell, who would start his radio broadcasts with, "Good evening, Mr. and Mrs. America, from border to border and coast to coast and all the ships at sea."
The three brothers Gerhardt are all shades of the brothers Corleone in The Godfather. Dod, like Sonny, is the hotheaded and impulsively violent eldest son; Bear, like Michael, is the more cunning brother who covets a life outside of organised crime but ultimately rises to the top; and Rye, like Fredo, is alienated from the family for his lack of experience and ultimately makes things worse for everyone with his poorly-thought-out schemes. Likewise, Otto is parallel with Vito Corleone, who himself suffers ill health and becomes frail in his old age.
