When Elliot asks Quentin for the button to travel back to Fillory, Quentin tells him he bargained the button to a dragon so they could travel to the underworld. Elliot replies "You gave our only means of traveling to Fillory to f-ing Trogdor?" Trogdor is a dragon in a skit from the popular early 2000s animated comedy website called Homestar Runner.
In this episode Josh invokes "hakuna-matata", a Swahili phrase meaning "no problem" or "no worries". It is also heard often in "The Lion King".
At 18:46 Sylvia says "... I'm Team Sarah Connor". Sarah Connor is the original female protagonist in the Terminator franchise.
When Umber asks Quentin and Eliot their opinions to help him create his new world, he mentions turtles. This is a likely reference to the Discworld series, a world which is carried on the back of a giant turtle, A'tuin.