Kate's aunt is named Moira Brandon. In the comics, Brandon is an aged former film actress who sold her home to the Avengers for use as their west coast headquarters. After helping Hawkeye and Mockingbird on a case, she is made an honorary Avenger. The large film posters in the apartment are for fake movies that Brandon starred in.
First appearing in Hawkeye (Vol. 4) #14, Detective Caudle was a detective for the Santa Monica Police Department portrayed as a bald white male. Kate Bishop constantly bothered him when she was trying to bring Flynt Ward to justice. At one point in the investigation, Caudle threatened to arrest her because of her persistent meddling. Ward was eventually arrested but Caudle had a sinking feeling that their "charmingly antagonistic relationship" would not end after that case.
Kate's aunt's apartment has a mezuzah on the door, meaning she's jewish.
The heads and silver robot in the poster for fictitious movie "Creature of the Dark Galaxy" are taken from the cover of February 1953 "Space Science Fiction" magazine.
Kate's aunt's place is ten blocks away is the same building that Natalie Portman's character, Mathilda, lived in with her family in Léon: The Professional (1994). Kate's aunt's apartment door is Mathilda's family apartment door. The interior of the apartment building is the Hotel Chelsea, the hotel where Jean Reno's character Leon lived. Kate points out and even pushes the ringer button for Leon's apartment, 6D, in her random button pushing to get someone to unlock the outer door while pretending to be a pizza delivery. The small grocery store attached to the building where Leon bought milk is a hardware store in Hawkeye.