During the series run, Florence Henderson lobbied the producers constantly to allow Carol Brady to get out into the workforce. Henderson thought this would be more in line with how she was in real life. The producers kept the character of Carol Brady unemployed, though she frequently did volunteer work and fundraising for charity.
A scene in The Honeymoon (1969) makes it clear Mike's first wife had died, making him a widower, but the status of Carol's first marriage was kept a secret. Creator Sherwood Schwartz maintained Carol was divorced from her first husband, but nothing about it was mentioned on the series. At that time, divorce was a subject matter that was still considered largely taboo for television, particularly a series aimed at family audiences.
The sliding glass door in the back of the Brady house actually never had glass in it. It was simply put on the sliders with no glass so as to prevent glares from lighting while filming.
Robert Reed was a closeted gay man. Florence Henderson noticed early on that he appeared uncomfortable acting romantically with her, and he admitted the truth to her privately. They worked around it, rehearsing kissing and hugging scenes off-camera, so they would look more natural when it came time to film them. The entire cast kept Reed's sexual orientation a secret until after his death.
Robert Reed strongly disliked his role as Mike Brady. He claimed he only took the part because Sherwood Schwartz told him the show would be a serious, boundary-pushing look at modern day family life. Schwartz considered the possibility of either hiring a new actor to play Mike or killing off the character altogether, if the series were renewed for a sixth season. Reed stayed with the series (and subsequent reunion spin-offs) out of loyalty to the kids.