Very often Buffy was shown with her 'Mrs. Beasley' doll. That became the highlight of the show so much a line of replica Mrs. Beasley dolls was launched. It sold well, and continued to for years after the series' cancellation.
Producer Don Fedderson insisted that the character of Buffy remain perpetually six years old, even as Anissa Jones, the actress playing her, grew into her teens. In promotional appearances, Jones was still required to bind her chest and carry the Mrs. Beasley doll. This dehumanizing treatment is thought to have contributed to Jones feeling too typecast to continue her acting career. This discouragement also contributed to her dissolute behavior in her teen years until she died of a drug overdose at the age of 18. As her mistreatment as a child actor not allowed to act her true age became public knowledge, it became informally accepted from then on in Hollywood that all child actors in live-action roles must be allowed to grow up normally and have their characters reflect that progress.
Cissy, Buffy and Jody were living in Terre Haute, Indiana, where Bill and his brother grew up, before moving in with Bill and French.
In the episode that Buffy broke her leg, Anissa Jones had really broken her leg and the writers came up with the script for that episode in one day.
Interestingly, the show was set in the same television "universe" as My Three Sons (1960) and To Rome with Love (1969) due to the fact that all three shows were produced by the same production company. In fact, the characters of Mr. French, Buffy and Jody made a crossover appearance on "To Rome with Love". However, none of the cast from "Family Affair" ever appeared on "My Three Sons".