Christopher Plover says, "about the trees of Fillory. You see, there are many, but in truth, only one. ... The roots of the trees of Fillory intertwine, such that they become one." Quaking aspen trees are like this: they grow in clonal colonies which appear to be individual trees, but all the trees are genetically identical clones growing from a single shared root system, so each clonal colony is considered to be a single organism. One, called Pando, is the heaviest and oldest known living thing, estimated to be around 80,000 years old.
When Penny and Plum travel back to 1920 Brakebills, they see a photo of student "Eric Lamontagne" on the Dean's List of Excellence on a bulletin board on the library wall. Eric Lamontagne is the Production Sound Mixer for this season of The Magicians.
When Penny and Plum travel to 1998, the student they stop in the hallways says they're going to go read "The Starr Report." The Starr Report is an official government report about the investigation into Bill Clinton, and, most famously, his relationship with Monica Lewinsky.
Stella Maeve who plays Julia and was pregnant in this episode was actually pregnant in real life at the time of filming.
Eliot offers Julia some cider, but he is not attempting to make the pregnant woman drink alcohol. This is because in American English cider is merely sweetened apple juice, even though in English English cider is fermented apple juice.