Jean Vander Pyl was pregnant at the time of recording and gave birth to her son on the day "The Blessed Event" originally aired.
This was the first time in an animated TV series where a character got pregnant.
The first episode where Wilma and Fred share a double bed instead of two single beds.
Originally, Fred and Wilma were going to have a son named Fred, Jr., but it was later decided their baby should be a girl as it could be a bigger target for merchandise.
Wilma jokes that she and Fred's baby will be 7 years old by the time they finally get to the hospital due to how long it was taking Fred and Barney to get her there. This would be considered appropriate based on television norms of the time. Even though The Flintstones was originally an adult prime-time cartoon when it first aired (hence the advertisements for Winston cigarettes with the main characters in it), the real truth of where babies come from was still a taboo subject for television at the time, which made it easy to retro-cede the cartoon into being a child's cartoon years later in syndication. Hence it is assumed (especially by many children watching) that they were going to the hospital to "pick up" their baby based on the joke. In modern times, Wilma would've quipped that she was going to end up actually giving birth in the car if they didn't get her to the hospital in time.