Chapter One - S1-E1
Continuity mistake: At the end of the episode, Perry comes to a realization about the case, putting together the various photos and clippings as TV detectives do. When he stands up from the floor, though, the pieces, however, change place (just look at the photo that partially covers the "Horror" headline in close-up, but is way below it in the overhead shot). (00:53:05)
Chapter Two - S1-E2
Continuity mistake: When Perry is trying to get Pete to help and offers him $23, he holds the money between his fingers facing up. But in shots from behind Perry, the money is upside down.
Chapter Five - S1-E5
Continuity mistake: When Sister Alice is preaching with the man in the wheelchair is on stage, the way she holds her Bible changes in between shots. For example, after she lists those who were there, her hand is on the Bible but it's closed around her hand. In the next shot, it's closed, and she's holding it on the side. Then it's fully open.