Actor Allusion: In part 2 of the Grand Canyon arc, Alice says the Native American word for "hi" will come in handy if she ever runs into Tonto. In part 3, they meet a native boy whose father is played by Jay Siverheels, who played Tonto.
Bad Bad Acting / Lost in Character: In And Now a Word From Our Sponsor; how the Bradys perform on the day of shooting, disgusting Farnum and leading him to fire them.
Confessions; Confessions: As with the even-more famous "Marcia, Marcia, Marcia!", the lines "Mom's favorite vase!" and "Mom always said don't play ball in the house" are uttered once. (They are repeated, yes, but through Peter's nightmare.)
Cast Incest: Barry Williams (Greg) went out to dinner once with Florence Henderson (his TV-(step)mom) and the media made a bigger deal out of it than it actually was. A full-fledged relationship did not come of it. Barry Williams and Maureen McCormick also got hot and heavy, as did Chris Knight and Eve Plumb. Finally, Mike Lookinland and Susan Olsen had a fake marriage as little kids, which ended when Mike developed a crush on Eve.
Mike and Susan dissolved their fake marriage with a fake divorce, which they figured was doing the marriage ceremony backwards.
The Danza: Linda Gibboney plays Sandy's cousin Linda in Peter and the Wolf.
Fatal Method Acting: Averted in The Cincinnati Kids. Had Robert Reed not suggested that a test run was done first before filming the scene where the family rides the Racer roller coaster, one of his fellow cast member would have had their head smashed (and likely killed) by a camera that wasn't properly mounted on the train car.
First Appearance: Of Sam Franklin, the owner of Sam's Butcher Shop where the Bradys get all their meat and Alice finds her boyfriend and future husband. Veteran character actor Allan Melvin took on what became one of his two signature roles (the other being Barney Hefner in All in the Family).
Fans of Gunsmoke might recognize Howard Culver, who played the recurring role of the Dodge City Hotel clerk Howie Uzzell. He's Mr. Crawford in this installment.
Hal Smith, best known as town drunk Otis Campbell in The Andy Griffith Show, is a department store Santa who promises Cindy that her mother will get her voice back by Christmas. Smith later appeared in Season 2's The Winner as the "Cartoon King".
The Season 1 episode Is There a Doctor in the House has this trope appear twice, both by sitcom parents – Herbert Anderson (Henry Mitchell, father of the title character in the U.S. live-action TV adaptation of Dennis the Menace) and Marion Ross (later Mrs. Cunningham on Happy Days).
Fran Ryan (as Mrs. Hunsaker) was a familiar character actor on TV shows from the 1960s through 1980s.
Hope Sherwood (daughter of series creator Sherwood Schwartz), who would appear twice later in the series as Greg's on-again, off-again girlfriend Rachel.
E.G. Marshall, Robert Reed's co-star in their earlier series The Defenders (he played the cantankerous, no-nonsense Mr. Randolph).
Paul Sorensen, who played Mr. Hinton, is perhaps best known to newer audiences for his recurring role (34 episodes) as Andy Bradley, owner of one of Ewing Oil's rival cartels, on the original Dallas.
Marcia Wallace plays the part of a department store clerk who sells Jan her brunette wig. Wallace went on to bigger and better things: a regular role on The Bob Newhart Show (receptionist Carol Kester), a regular gig on various game shows (most notably Match Game) and – in fitting the "Hey, It's That Voice!" trope – the regular role as Edna Krabappel-Flanders on The Simpsons.
Pamelyn Ferdin (best known as the 4th voice of Lucy Van Pelt in the Peanuts specials) also appears as, interestingly, Lucy Winters.
Chris Beaumont, but moreso to Brady Bunch fans than anything, as he's not particularly well known outside of his four appearances throughout the series, all as various teenagers. This was the first, playing a high school senior whom Greg tries to emulate. He'd later play a slick-talking salesman who sells Greg a lemon of a classic car, one of Greg's college friends and (finally) a rival high school quarterback whom doesn't trust his scouts and resorts to cheating.
Stephen Dunne, who was a host of Truth or Consequences, his work of course being greatly overshadowed by that of Bob Barker.
Former Mr. Magoo voice and Gilligan's Island star Jim Backus makes his first Brady appearance as the prospector. He later returns in The Hustler as he plays Mr. Matthews, Mike's boss.
Jay Silverheels as Chief Eagle Cloud. Fans of the original TV version of "The Lone Ranger" knew him as Tonto.
Charles Martin Smith: Remember Toad from American Graffiti? Then you'll know Ronnie, the nerdy guy whom Greg wants to unload his piece-of-junk car on.
Paul Winchell, the ventriloquist behind Jerry Mahoney and voice of countless Hanna-Barbera villians (Dick Dastardly and (later) Gargamel among them), and inventor of the artificial heart.
Imogene Coca, the comedienne best known for her role opposite Sid Caesar on Your Show of Shows.
Sam the butcher is played by Allan Melvin, who is best known as the voice of Magilla Gorilla.
Method Acting: And Now a Word From Our Sponsor displays this to the extreme, particularly by Mike and Carol after they take lessons from acting coach Myrna Carter, who is a bad, bad actress and couldn't teach a pencil how to draw.
This is not true. This may be the only reason he stayed with the show, but he said before he died that the show was pitched to him as being more adult and less like Gilligan's Island. That is why he agreed to do it.
Also, as a Paramount contract player during the waning days of the studio system, he was obligated to do the pilot.
Real-Life Relative: Robert Reed's daughter in an episode centering on the girls having a sleepover.
Sherwood Schwartz's daughter, in the same episode.
The Underground Movie: Super8 movie cameras were the in thing in 1970, and the fact that this is a sound camera made it even cooler. Of course, 8-mm films and the projectors used to play the films have long since bit the dust, replaced by video cameras and eventually camera phones. Additionally, until the advent of today's iPads (including those with movie-making applications) being issued to students, movies and videos as school projects was relatively novel.
As well as Cindy in A Very Brady Christmas and Marcia in The Bradys. The Brady Girls Get Married was the only project which reunited the entire original cast.
The Mexican Spanish dub of the TV series suffered one of the biggest casting shifts ever: Only the first three seasons were dubbed in Spanish in the 70s, since the series was canceled possibly due to low ratings in Mexico. The last two seasons weren't dubbed until the 2000s (about 26 years after the TV series ended both in the U.S. and when the series was canceled in Mexico) and when they dubbed the last seasons, they have to replace the entire cast, since almost all the original voice cast are retired from voice acting or died.
Starting with midway through this episode (due to the real Tiger's death before the essential scenes were taped), and continuing through to his final appearance in late 1970, a number of dogs played "Tiger." None of them worked out, and since the focus was more on the human members of the family, Tiger was ultimately retired.
Write Who You Know: In And Now a Word From Our Sponsor; this is how Skip Farnum envisioned the Bradys when he hired them, expecting natural performances.