Goofs

At 25:32, the ketchup bottle has ketchup almost all the way up the bottle. At 25:39, the bottle is less than half full.

Mr. Wrench asks Bruce Gold why there's no library in town, but in the pilot Lester's prospective customer states that he works at the library. However, the young man did not say at which library he worked so it's possible he worked at the county library in a nearby town. Additionally, in the season finale, he is to have a new job at an auto dealership, so it's possible he was laid off before the events of this episode. (In actuality, Bemidji does have a public library.)

At Vern Thurman's graveside and at the wake, Officers Solverson and Oswalt surely would have honored the tradition of wearing a black band over their shields, a long-standing expression of mourning for a fallen officer. Perhaps this was artistic license, but it appears to be an oversight.

When Lorne Malvo is walking out of the supermarket, a Scotiabank is visible in the background. Scotiabank is a Canadian bank with no branches in Minnesota.

Since the Filming Locations and the closing credits both say Fargo Season 1 was filmed in Calgary, Alberta, pointing it out isn't really a Goof.

Molly states she is 31 years old, making her birth year 1975 but in Season 2 she is 6 years old in 1979, making her birth year 1973.

Continuity doesn't apply going front to back. A Continuity Goof can't come from the future.

When Molly is standing in the cemetery at Vern's grave, in the establishing shot there is a gravestone in the size, shape, and granite type of the Commonwealth War Graves Commission, the organization that places gravestones for British Commonwealth veterans and war dead. Given that the cemetery is in a cold climate and there is a Commonwealth gravestone, it's clear the cemetery is in Canada, not the United States.

Minnesota *is* in a cold climate. Since the Filming Locations and the closing credits both say Fargo (2014) was filmed in Calgary, Alberta, pointing it out isn't really a Goof.

Lester's wife's car is an Acura CSX, a model that was not sold and generally can't be titled in the US.

The events took place in 2006, but when Lorne Malvo is arriving at the Phoenix Farms store, a Kia Optima, which began production in 2010, is visible in the parking lot.

Stavros Milos (Oliver Platt) calls himself "La mercado rey" but the correct translation of "The market king" would be "El rey del mercado" in Spanish.

In 2006, barely 5% of the population of Minnesota was Spanish. Little wonder Milos (not a Spanish name) isn't fluent.