The cutaway that Stewie describes at the mansion party is in reference to Donald Sterling dating V. Stiviano. He is dressed like her in that scene as he is running away from the paparazzi.
The Peter Catcher cutaway is based on the 'Child Catcher' from the 1968 movie 'Chitty Chitty Bang Bang'. The Child Catcher has generally topped the charts of scariest movie villains and even got voted (by CBBC) as the scariest children's book villain even though he was not in the book but created purely for the film.
Stewie's preschool toilet has a sign, "If it's brown, let it mellow". A few decades ago, when water conservation first became an issue in the southwest, folks noted the absurdity of using two gallons of water to flush each cup of urine. "If it's yellow let it mellow. If it's brown flush it brown." could easily save a standard household over 10,000 gallons of water per year.
Stewie, to impress a rich kid, mentions a plan to return to his personal mansion and kill a wrestler. In 1996 David Schultz, an Olympic wrestler, was murdered by John E. du Pont, a multi-multi millionaire. J. E. du P. was too rich to be considered totally bug-nuts crazy. So this charmingly eccentric gentleman terrorized his neighbors by running around their properties in his fully operational Sherman battle tank before shooting his wrestler guest (under the belief the wrestler was part on an international assassination plot).
Peter's old girlfriend's name is Gretchen Mercer; Seth MacFarlane [Peter] plays Capt. Ed Mercer on his show The Orville.