The book Mr. Poe has is the reverse side of the book jacket for the book Lemony Snicket: The Unauthorized Autobiography.
Mrs. Bass, Mr. Remora, and the gym teacher, Ms. Tench, are named after types of fish. A group of fish is called a school.
The banner in the cafeteria says, "Remember, you will diet." The school motto is, "Remember, you will die."
The painting of Barrymore Feint is actually the show's director, Barry Sonnenfeld. Barrymore Feint would presumably be related to Ellington Feint, from the All the Wrong Questions book series by Lemony Snicket.
The librarian says, "In every library, there is a single book to answer the question that burns like a fire in the mind." "They say in every library there is a single book that can answer the question that burns like a fire in the mind" is the advice that librarian Dashiell Qwerty gives teenage Lemony Snicket in the book Who Could That Be at This Hour.