In a flashback, Peter meets Timer, “the Cheese Guy”, a character who appeared in the ABC network’s 1970s public service announcements on nutrition. 
The doctor shows Peter where his test results place him in terms of intelligence. His chart shows “Retarded” below “Average”, but above “Creationist”. The scene is a reference to a similar scene in Forrest Gump.
The scene at the dinner table in which Peter introduces his state appointed inspirational social worker named Verne is a reference to the 1988 film Rain Man in which the character Verne is Raymond Babbitt's "main man".
A voiceover counts the prostitutes Peter brings to Cleveland’s house. This is a parody of the Baker films.
"I'm A Tumor" is to the tune of “Rock Me Amadeus” by Falco.
While Peter is defending himself in court, he lists off celebrities that have been exposed as unfit parents, specifically Bing Crosby who reportedly beat his sons, Joan Crawford of the film Mommie Dearest and the Ramsey family.
The "Peter is Slow" musical number, cut from the aired episode but featured in the DVD release, is a reference to the "Telephone Hour" number from the movie version of the musical, Bye Bye Birdie.