As of this episode, according to Claire Ivey, John Nolan joined the L.A.P.D. 2 years ago. Since the Academy takes 6 months, Nolan was a rookie for almost a year and a half.
Aaron Thorsen's backstory appears to be based on the real life trial and exoneration of Amanda Knox. Knox wrote an essay not long before the episode referencing the film Stillwater and the way that stories inspired by her (usually created without consulting or informing Knox) have negatively affected her life. It is unclear if Rookie writers consulted or informed Knox for this character.
Tricia Helfer and Nathon Fillion worked together as voice talent in Halo 3:ODST (2009) where their characters were romantically involved.