Despite being the 243rd episode by broadcast order, this episode was originally marketed to be the 250th episode, an honor later given to "Fighting Irish". 
Stewie's reaction to Brian's gift in "Christmas Guy" is to question if they are expecting. The DVD commentary for that episode confirms that this led to the creation of this one.
Meg is mentioned but does not appear in this episode. Chris appears but has no lines.
All of Stewie and Brian's children are half-human/half-dog hybrids, yet Dylan, another biological child of Brian's, is seemingly entirely human.
The song played during the photo montage is "(You're) Having My Baby" by Paul Anka.
The song playing on the jukebox is "You Give Love a Bad Name" by Bon Jovi.
The song played during Peter's viral video is "Hey There Delilah" by Plain White T's.
The films that Joe tries to do impressions from are Jerry Maguire, Austin Powers, Good Morning Vietnam and the 1989 version of Batman.
Stewie's request for Brian to change the cat litter is related to a suppressed immune system commonly found in pregnant women.
In an uncensored extended scene, Peter tries to defecate while sitting in Joe's hot tub with Cleveland and Quagmire as Joe films. But when Peter has a movement, to Cleveland and Quagmire's horror, the hot tub fills with blood. When they inform him that it is supposed to be brown, Peter recognizes it as the color of his pee.
In another bonus scene, Stewie asks Dr. Hartman if they should send the bill to President Barack Obama following his prenatal care examination. A cutaway to Obama shows him making one of his speeches about the benefit of the Affordable Care Act, commonly known as "Obamacare." He uses Stewie's persona of "Rayleen Griffin" as one of his examples of people who would benefit. In the audience, Stewie sits with Michelle Obama and asks to talk with her about the place where they have been given a room while in town.