The title of the episode is a reference to the television series and film Mission: Impossible.
Stewie’s dialog after opening the fridge is taken verbatim from an old Sunny Delight commercial where kids root around in the refrigerator and pick Sunny D over the other drinks.
Stewie watches an episode of The Smurfs which spoofs the way the characters use the word smurf as a euphemism for an endless number of words.
Before Peter and Lois leave the kids with Quagmire, he mumbles “Well, in accordance with Megan’s Law, I’m obligated to inform you...” Megan’s Law, named after seven-year-old rape and murder victim Megan Kanka, is a New Jersey law requiring convicted sex offenders to identify themselves to neighbors. The term is used colloquially to refer to similar laws in other states.
Peter asks Carol to say “David Banner, I just slashed your tires” before he rips through one of Ted’s shirts. This is meant to mimic the transformation of David Banner into The Incredible Hulk in the 1977-82 Hulk TV series.
Peter finds the Griffins’ pet rock, which were a popular 1970s trend
The way Peter stops at a drive-thru while rushing Carol to the hospital is a similar to a gag to the television series Freakazoid!. While transporting Freakazoid to the hospital, Sgt. Cosgrove does the exact same thing.
Stewie storms back in the room and shouts “WHAT?!” a la Ralph Kramden on The Honeymooners, after finally realizing what he thinks of Peter and Lois having another baby.
A cutaway shows the Brady family abusing the youngest boy Bobby after Cousin Oliver arrives. The character was added during the last season of The Brady Bunch because the younger children on the show had grown older and were not capable of the same “cute kid” humor they once were.
Stewie's line "As God is my witness, Peter and Lois shall not conceive" is modified from Gone with the Wind. Forced to survive on turnips after the destruction of the family plantation, Scarlett vows "As God is my witness, I'll never be hungry again!"
After Cleveland sees Stewie escape the Peter robot, he says “I see nothing, nothing!” in a German accent. This was a catch phrase of Sergeant Schultz, a bumbling German Sergeant, on the 1960s sitcom Hogan's Heroes, in which a group of Allied prisoners of war sabotage the German war effort from a POW camp. Schultz, who was sympathetic to the Allies, shouted the phrase to indicate that he would refuse to report the prisoners’ shenanigans to his military superiors.
Stewie’s vessel is similar in function to that in the 1966 film Fantastic Voyage.
Stewie’s air battle with Peter’s sperm parodies that of the Millennium Falcon and the ships of the Galactic Empire in Star Wars Episode VI: Return of the Jedi with one of Peter’s testicles representing the Death Star.