When Peter is messing with the remote, he changes Stewie into,
Bart Simpson - The Simpsons.
Rallo Tubbs - The Cleveland Show.
Bobby Hill - King of the Hill.
Steve Smith - American Dad.
Allen Gregory - Allen Gregory.
Louise Belcher - Bob's Burgers.
Bender Bending Rodriguez - Futurama.
Manny Delgado - Modern Family.
The picture on Peter's passport is Steve Buscemi.
The title refers to an earlier episode in which Peter grows a mustache and believes it gives him the ability to speak Italian, but all he says is "boopa de boppa dee" and similar gibberish.
Chris asking his large-breasted teacher if he's in calculus is a nod to the Italian word "seno," which means both "sine" and "breast."