Continuity mistake: Most of Season 1 takes place in January of 2006, while Season 2 takes place in March of 1979. Molly mentions near the beginning of Season 1 that she's 31, and her father confirms this in episode 10 by mentioning that she was 4 years old during the events of the Sioux Falls massacre (season 2). In season 2, Molly's mother mentioned in episodes 1 and 4 that she's 6. It's also revealed in a flashback scene in episode 10 that she graduated high school in 1991 (most people are 17 or 18 when graduating high school). If you do the math, you'll see that there's an inconsistency in her age between Seasons 1 and 2. Apparently, 2 years were added to her age in Season 2.
Continuity mistake: When Gus arrives to visit Molly in the hospital, he brings her a bouquet of flowers. He sets the flowers on the roll-away table stationed over the end of the bed, and the blooms are facing towards the window. When the scene cuts to a different angle as he is walking toward Molly, the bouquet is now completely turned around and the stems are pointing at the window, even though Gus did not touch them again.
Trivia: In the flashback scene at the beginning of Episode 4, the young Stavros Milos finds a case of money buried in the snow, next to a fence on the road where his car runs out of gas. This is the same case that Carl Showalter buried there in the 1996 Fargo movie. It was the ransom money for Jerry Lungegard's wife. Stavros apparently used it to start his grocery business.