In the show's opening (beginning with the sixth season), a toddler walks up to Joyce DeWitt as she is feeding a goat. The toddler is Jason Ritter (son of John Ritter). This is revealed by DeWitt in a bonus feature of the Season 4 DVD.
During the earlier seasons' opening credits, the brunette walking by the beach who causes Jack to fall off his bike is Suzanne Somers in a wig.
In the biography "Andy and Don" by Daniel de Vise, Don Knotts admits he was very nervous the first day on the set, because he'd never done a three camera style sitcom before. The Andy Griffith Show (1960) had employed a single camera format. "They were all much younger than me...and they were all good." But when he showed up on set his fears were dispelled when the studio audience immediately gave him a ten minute standing ovation.
At the end of season three, Mr. Roper reveals that he sold the building, and the Ropers are moving. Mrs. Roper is hesitant. In real life, Audra Lindley was excited about doing a spin-off, while Norman Fell didn't want to leave Three's Company. It took him almost six months to agree.