The women that Bart meets at the asylum is a reference to Nurse Ratched of One Flew Over the Cuckoo's Nest (1975); a film about a person who fakes insanity in a mental institution.
Lisa said she would build a solar car in Lisa Goes Gaga (2012). In this episode she does exactly that.
This episode reveals that Lisa speaks French fluently. This means every speaking member of the Simpson family, except for Homer, speaks French: Bart becomes fluent after spending time in France in The Crepes of Wrath (1990), and Marge tutors the subject in The Way We Was (1991).