Continuity mistake: In the beginning of the episode when Eric and Jake are riding in the car, Jake asks Eric if the shotgun is loaded, and he says yes. The gun in pointed up towards the roof of the car. The shot changes and the gun is gone, then switches back and it's back on Eric's lap.
Continuity mistake: After Jake has seen Hawkins through the scope, he lowers it down to his hip in the long shot. Cut to a close-up of Jake, and he is suddenly holding the scope much higher, at shoulder height, without any time to move it back up between shots.
Continuity mistake: When Gray and Jimmy are questioning the Hawkins family, Jimmy is wearing his brown uniform jacket. But in the scene where Gray is asking if Jimmy can search the house, Jimmy's jacket disappears for an instant, just after Gray has said "Just a question of being thorough". Allison Hawkins makes a remark about this being Kansas, not Soviet Russia, and as the camera comes back to Jimmy, his jacket is back on.