Zach says he's only ever failed three tests: scoliosis, Turing, and lice. The Turing test was developed for early computers to see if they could exhibit human intelligence. Since Zach failed the test he failed to respond like a human.
Jim Gaffigan plays Officer Krupke in this episode. Officer Krupke is the policeman in West Side Story, who the Jets sing Gee, Officer Krupke about.
When Lillian says "it's about your future" she has just arrived in a Delorean. The Delorean was famously used in the Back to the Future films and Zach is wearing the same puffed vest as Marty McFly.
Dean Koontz is a sly reference to horror writer Dean R Koontz
Carol Kane and Peter Riegert both starred in films set in New York's Lower East Side directed by Joan Micklin Silver: Hester Street and Crossing Delancey, respectively.