This page contains trivia for "Trapper Keeper". Remember, trivia must be factual, provable, and it is always best to cite your source for not-so-obvious trivia. If you would like to dispute a trivia point, please discuss it in the article comments.
This is the first episode where Mr. Garrison is shown as a teacher for the kindergarten class.
After BSM-471 has revealed its true identity, Kyle and Stan keep calling him Bill Cosby.
They came up with idea for the episode while on a houseboat in Lake Powell, Colorado with some friends and Trey's grandmother.
BSM-471 speaking mannerism was based on staff writer Kyle McCulloch who would speak in a similar manner to the staff during the writer's retreat as a joke. He also provided BSM-471's voice for the episode.
The voice of Filmore Anderson was done the by son of South Park producer, Frank C. Agnone II.
They mention that they have to hire new kids for the kindergarten class often as they don't sound as cute as they get older. They also point out that they had already gone through multiple actors for Ike.
The title of the episode as well as the source of problems for the boys is a reference to a Trapper Keeper, a loose leaf binder that was popular among kids from the 1970s until the 1990s.
References to Popular Culture
The whole concept of sending someone to the past to get rid of a robotic enemy is a reference to the Terminator films.
BSM-471's clothing is similar to Kyle Reese from the first Terminator film.
The idea of the Trapper Keeper taking over the world and leading to an apocalyptic war is similar to the supercomputer Skynet taking over, leading to Judgement Day.
In the creator's commentary, Matt and Trey mention that one of the girls is named Flora and was being indecisive, in reference to the state of Florida being a point of contention during the election. The state was in the middle of doing a recount when this episode was created.
Rosie O'Donnell coming to the classroom is a reference to O'Donnell and other celebrities signing a petition demanding for a re vote in Florida in the hopes of giving the election to Al Gore. 
Jesse Jackson entering the kindergarten classroom and claiming that African-Americans were not represented in the election is a reference to him traveling to Florida after the election to protest and demand an investigation regarding accusations of racism. This stemmed from claims that black voters in Florida were not able to vote due to their names accidentally being purged from the voter registrar, having to deal with antiquated voting machines and long lines, and accusations of police officers deliberately stopping black voters on their way to the polling places. 
The scene where Kyle is floating on the inside of the massive trapper keeper is an homage to HAL 9000 of the movie 2001: A Space Odyssey.
BSM-471's secondary name is a reference to comedian / actor Bill Cosby.
Cartman says, "I don't know dude, I'm not supposed to have male friends that are over thirty; I kinda got screwed on that one", which is a reference to the events in "Cartman Joins NAMBLA".
After Cartman chases down Bill Cosby (BSM-471), Kyle says, "Damn! I thought fourth grade was gonna be different". This is a reference to the previous episode when they realized during Ms. Choksondik's aesop that fourth grade will be just the same as third grade.
Filmore says that Carlos is absent, but when the absent kid is in the classroom, Garrison calls him Billy.
It's possible that Carlos was Billy's nickname.
When the trapper keeper hybrids with Cartman, Kyle and Stan both call "not it!" to break down the door. When Kenny rushes the door, though, Trapper-Cartman smashes the door against the opposite wall, crushing Kenny in between.
After getting into the police car, Bill Cosby suddenly has a wound on his face for no reason.