The poster on Randall's side of the dorm room in Monsters University is an inspirational poster about the "winds of change." In Monsters Inc., Randall talks to Mike and Sully about the winds of change. It's like how when I want to intimidate my co-workers, I talk to them about John Belushi wearing a college sweater.
Whenever Mother Gothel shows Rapunzel any affection, it's always directed at Rapunzel's hair, not at Rapunzel herself. That's because her hair keeps Mother Gothel looking young. Hey, Mother Gothel, any relation to Melisandre on Game of Thrones?