While Mike was a widower before he met Carol, Carol was supposed to be a divorcee. The eventual Mrs. Brady referred to her maiden and former married name once in one episode but divorce was still taboo enough for network television that they never referred to her divorce outright.
Because television networks didn’t allow even the hint of one of their characters going number 1 or number 2, the Brady Bunch kids’ bathroom had no toilet. The producers found it easier to never include one than show a bit of a toilet and use tricky camera angles.
Maureen McCormick (Marcia) and Barry Williams (Greg) actually dated for a short period of time. They were apparently actually each other’s first kiss. Producers put an end to the romance for a number of reasons — with the main one being they were both teenagers and a messy breakup could have ruined the show.