In episode 5, when Stephanie Boggs is speaking to Tate, she tells him that before he killed her, he asked if she believed in God. She says that she told him yes, which "wasn't even true." In this episode during the flashback to Tate's shooting, he does not speak to her, or to any of his victims.
During therapy Derrick says, "I binge eat, I smoke like a fish. Lately it's gotten a lot worse." - either he flubbed the line or there was a decision not to steer the problem towards alcoholism by using the correct term "drinking like a fish".
In ep#1.5 Steph tells Tate: "You asked me if I believed in God, and you put a gun to my head. I said yes. And then, you pulled the trigger."
But in the next episode#1.6, Tate shooting in school is shown with details, yet when he approached Steph, nothing is said, only his footsteps are heard and then the deadly fire shots.
The goof item below may give away important plot points.
The wounds given to some of the students during the school shooting are inconsistent with how they appear as ghosts. Specifically Kyle Greenwell (the jock), shown to have a small, single gunshot wound to the forehead as a ghost, is shown being shot with a shotgun.