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 Greta sits down with the shotgun, it is pointing directly at Lou, horizontally angled. However, after a cut, the gun is suddenly pointing diagonally, at an angle. It is also strange that Lou, a former police officer, doesn't caution his novice granddaughter against pointing a loaded gun at him. (00:40:15)
Continuity mistake: During the sequence in the woods where Bear shoots Simone, the sun angle changes numerous times. It is afternoon throughout the first half and then the sun is setting while she is pleading for her life. When Bear gets back to his truck the sun is overhead again.
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.
Continuity mistake: The antenna on the back of Ted Danson's police car is not present when he's talking to the other officer. When he gets back to the station it is back on the car. Also, the other officer's vehicle doesn't have an antenna. How would their radios work?