After 'Jan' runs away from home, she is seen walking a dark city street with provocative music playing in the background. This is an in-joke reference to the original Jan Brady, Eve Plumb. Plumb famously portrayed a runaway-turned-prostitute in the TV-movie "Dawn: Portrait of a Teenage Runaway".
As he heads off to his business meeting, Carol Brady tells her husband, Mike, to "Go get 'em, Tiger", and then wonders to herself "Tiger, Tiger: what ever happened to that dog?" Tiger was the name of the Bradys' dog in the TV series. But, after the first two seasons, the dog was never seen again, even though his dog house was still out back. The movie is supposed to take place in the later seasons. So, that line is an inside joke to the show.
The producers had unsuccessfully sought to use the original house that was used for exterior shots from the original Brady Bunch series, but the owners of the home in Studio City, California refused due to many years of seeking fans who've trespassed. Instead, they found a similar home in nearby Encino, and erected a facade, and actually filmed scenes in the front yard.
A lot of scenes shown in trailers were cut at the last minute due to objection from producer Sherwood Schwartz. These included a grunge band scene in the garage with Greg and Eric, and a seduction scene between Mrs. Dittmeyer and Peter.
Christopher Daniel Barnes, who plays Greg Brady here, was among the cast of the NBC TV series Day by Day (1988), as Ross Harper. In a memorable 1989 episode, Ross Harper falls asleep and dreams he is Chuck Brady, the "lost" Brady, in a very clever "Brady Bunch" reunion, with much of the original cast appearing.
Florence Henderson initially turned down her cameo, as she didn't like the scene she was to appear in. After test screenings criticized the absence of Henderson, the producers convinced her to appear under the condition that she would have some certain control over her scene. At that point, Henderson accepted.
Prior to the movie, Gary Cole starred on the TV series Midnight Caller. The supporting cast during the show's final season included Lisa Eilbacher, who guest starred in the Brady Bunch episode The Subject Is Noses, which was partly spoofed in the film.
Gary Cole, playing Mike Brady, went on to play Vice President Bob Russell in The West Wing (1999). Interestingly, the man pretending to be Carol Brady's first husband in A Very Brady Sequel (1996), Tim Matheson, also went on to play the Vice President John Hoynes in "The West Wing".