Susan Olsen (Cindy) was the only original cast member not to appear in the movie, because she decided to go on her honeymoon in Jamaica. She also found out that Paramount only had to deliver on five of the six "kids," and wanted to pay Olsen the least, which was all the more reason for her to turn down the film.
When Alice is meeting people at the airport, she initially approaches a young woman, incorrectly believing that she is Cindy, shortly before the real Cindy arrives. This is likely a reference to the fact that Cindy is not played by the actress who originally played her, Susan Olsen.
Mike Lookinland didn't dye his hair brown as he did during the original series, making this the first time Bobby was seen blond.
At the start of filming, Robert Reed, Barry Williams, Christopher Knight and Mike Lookinland all had mustaches. Producer Sherwood Schwartz insisted that at least two of them shave, or else, he joked he'd have to rename the film "A Very Brady Moustache." Christopher and Mike would shave their mustaches, while Robert and Barry would keep theirs.
While it was always very loosely implied but never explicitly stated in The Brady Bunch (1969) that the Bradys lived in the Los Angeles area, that implication is more pronounced in this movie as Alice is assigned to pick up some of the kids at the airport, exterior images of the airport being of LAX.
Mark Thompson, Brian Phelps: As "concerned onlookers" in the construction site scene. Thompson and Phelps were hosts of "The Mark & Brian Show" on radio station KLOS in Los Angeles. Their show was #1 in the Arbitron ratings when they made this uncredited appearance in the movie.