The BAU meets at the Diamond Bar Police Department. However, Diamond Bar does not have its own police department. The Los Angeles County Sheriff patrols the City of Diamond Bar.
The unsub presses "record" on his tape recorder before he starts his fantasy with Greta Thomas. Only the "record" button goes down. The "play" button for the recorder would have to go down with the record button to actually start recording.
Peter tortures his victims in the basement of his house. However, houses in Diamond Bar (as well as other cities in Southern California) do not have basements.
The unsub puts on an apron before beating up the victims. The apron shows bloodstains that have leaked through to the other side and is therefore not effective at keeping the stains from destroying the clothes underneath. With him being uptight and meticulous as he was, he would not be likely to wear an apron that doesn't prevent the leaking/staining (or wear a dirty apron at all).