Todd's drawing "pumped out kicks to outrun bullets" is a reference to Foster the People's similarly named hit "Pumped Up Kicks", a song about teenagers and gun violence.
When Bojack and Hollyhock arrive at the nursing home, the song "I Just Met My Perfect Match" plays in the background, first heard at the 50s-themed diner Bojack went to with Wanda in season 2.
When Lenny Turtletaub tells Princess Carolyn they may have to put Ms. Taken on the shelf next to a wacky vacation comedy about a klutzy babysitter, the film in question is titled Hurricane Sandy, and it stars Sandra Bullock. It is heavily implied by the film's title that it was pulled from theaters before it came out because of the real-life Hurricane Sandy incident that lasted from October 22, 2012 to November 2, 2012.