Ole Munch has many similarities to Gaear Grimsrud:
Gaear is a Swede, while Ole has a Norse name and is implied to be of Norse origin, based on his tale of traveling by longship.
He's hired to kidnap a housewife, just like Gaear, and his movements during the kidnapping attempt loosely follow Gaear's.
In a later episode, he requests pancakes, as Gaear does.
When Ole emerges from Irma's house to kill her son with an axe, it's shot exactly the same as when Gaear emerges from the cabin to kill Carl.
Dot's attempted kidnapping in her home plays similarly to, and in contrast to, the kidnapping scene in Fargo
In both series and film, each of the victims is watching TV and knitting on her sofa when she observes a masked man walk onto her porch, peek into the window, and crash through the door. Dot has already started running when the crooks break in, while Jean is taken completely by surprise.
The kidnappers are a laconic, larger man and a more talkative, weaselly man, both wearing masks. One breaks through the back door and the other enters through the front.
Both victims run upstairs and hide. When Dot emerges, however, she manages to keep the kidnappers at bay.
Indira Olmstead shares a surname with Marge Olmstead from the film. Both are city police officers.
Dot and Wayne are an inverse of Jerry and Jean from the film. Dot and Jean are both housewives of car salesmen, but Jean is the child of a rich father, while Wayne is the child of a rich mother.
Marge drives a car with a license plate starting with "DLR." In the film, a Brainerd cop mistakenly puts out a search for a car with a license starting with "DLR."
In his opening narration, Roy Tillman states that he's been the sheriff since the age of 25, and his father was sheriff before him. In No Country for Old Men, Ed Tom Bell states that he has been the sheriff since the age of 25, and he also comes from a family of lawmen.
The tracker that Gator installs on Ole Munch's car in "The Tender Trap" is the exact same one that Anton Chigurh uses.
Ole Munch also bears some similarities to Anton Chigurh:
He is dishevelled and has an unfashionable haircut.
He abides by a mysterious "code" rather than the laws or morals shared by other people.
He is seemingly immortal, or at least capable of escaping dangerous situations and healing from debilitating injuries.
Like Chigurh, he ends up threatening a confused elder person.
As with the ending of No Country For Old Men, Munch shows up at the home of the last person who could identify him, looking to settle this final score. Like Chigurh, Munch is briefly met with defiance from his potential victim, who is not impressed by his "code". Unlike Chigurh, the situation does not go as planned.
After the Time Skip in the finale, Munch appears in Dot's home the same way Chigurh finds Carla Jean Moss (though this time the outcome is sunnier).
Raising Arizona: Dot's nickname is a reference to Frances McDormand's character Dot, the housewife of HI's boss.
The Big Lebowski: When Roy asks Munch a philosophical question, Munch explains he's a nihilist who believes in nothing, like the German kidnappers in the film. This line is clearly inserted just as a nod to the film, since Munch later displays some pretty strong beliefs and even performs rituals.
There's a Nightmare Before Christmas poster on the school doors when Dot is being arrested at the PTA meeting.
The second episode has "This Is Halloween" playing as Gator and his partner arrive at the gas station where Ireland was killed.
When Gator and his men travel to Dot's neighborhood in episode 3 on Halloween, Gator wears a Jack Skellington mask while his accomplices dress as Lock, Barrel, and the Mayor of Halloweentown.
Before turning in for the night, Wayne asks Dot if she minds him watching Blue Bloods on his tablet. Moments later, in Dot's nightmares of Roy, there is a shot of Roy and his family seated around a dinner table like the Reagan family are for Sunday dinner in every episode of the show.
