Factual error: Peggy and Ed are hiding out in a cabin "just outside of Sioux Falls," but are somehow also close to Mt. Rushmore. Mt. Rushmore is near the western border of SD, Sioux Falls on the eastern border, more than 340 miles apart.
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?
Continuity mistake: In the parking lot outside the medical clinic where Otto Gerhardt just had an appointment, a large wet spot on the ground continually appears, disappears, changes shape, and sometimes has tire tracks running through it, then does not.
Rhinoceros - S2-E6
Continuity mistake: When Simone is on the phone with Mike, she puts the hand holding the phone down in her lap (so the back of her hand is touching her leg) to yell at the person in the room. When the shot changes, her hand and phone are now up at her chest.
Did You Do This? No, You Did It! - S2-E7
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.