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.
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.
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.
Richard Kline's role as Larry Dallas was originally meant to be a one-time guest appearance. But the producers enjoyed his chemistry with Ritter, so he became a recurring character and eventually a cast member.