The character of Shoshanna wasn't supposed to be recurring, but creator Lena Dunham liked Zosia Mamet's performance so much that kept her on the show as a regular, because they saw potential for exploring the character thanks to Mamet's talent.
Adam Driver had to repeatedly fly back and forth between New York and London between seasons 3 and 4 to film Star Wars: The Force Awakens (2015).
Jemima Kirke had to be convinced by Lena Dunham to take the role of Jessa, because Kirke didn't (and doesn't) have a long-term interest in acting, compared to her focus on her thriving career as a painter and artist.
All four main actress Lena Dunham, Jemima Kirke, Zosia Mamet, and Allison Williams have famous parents in some regard. Lena Dunham's parents are photographer Laurie Simmons and painter Carroll Dunham. Jemima Kirke's parents are fashion designer Lorraine Kirke and rock musician Simon Kirke. Zosia Mamet's father is writer David Mamet and mother is actress Lindsay Crouse. Allison Williams's father is NBC Nightly News anchor Brian Williams.
Allison Williams has a clause in her contract for this show stipulating that she will not do any full nudity.
The four titular characters - Hannah, Marnie, Jessa, and Shoshanna - only appear together in twelve scenes over the entire series.