Tate imitates shooting himself in the head with his finger is a direct reference to the 1976 film "Taxi Driver", where the main character Travis Bickle does the exact same thing in the same manner after his big shootout scene at the brothel near the end of the film
The trivia items below may give away important plot points.
The opening scene with Tate getting into the library and killing the students is similar to accounts of what happened at the Columbine Massacre during the period when the killers were in the library. Harris (one of the Columbine killers) shot a girl hiding under a desk, and a boy hiding behind the administration desk, this also happens in this scene. Furthermore, in the previous episode, one of Tate's victims, Steph Bogg, tells Tate that he asked her if she believed in God right before he shot her. This also allegedly happened in the Columbine shootings. Harris allegedly asked one of the victims the same question before shooting her. In this scene though, when Tate shoots Steph, he did not ask the question. It is unknown whether or not this is a goof, or whether it reflects the incident at Columbine, as there was some dispute after the massacre to whether or not Harris asked one of his victims the question.