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.
When Tate is surrounded by the SWAT team, as he gets the gun (no shots have been fired) you can see blood on Tates neck.
At approx. 19 minutes, the housekeeper is cooking the offal which clearly has just gone into the fry pan. Yet, within a few words, the offal is shown brown, as though it has finished cooking.
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.
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".
During the opening scene in 1994, the book cart used to barricade the library door holds "The Children's Blizzard" which was first published in 2004.