Author Existence Failure: Richard Leach, Sheryl's father in law and head of Lyrick Studios, passed away in June 2001 after selling the company to HiT Entertainment. The elder Leach financed the original three Barney videos out of his own pocket.
Beam Me Up, Scotty!: Contrary to popular criticisms, Barney has never stated that "strangers are friends you've never met."note This rumor started from a post to a Usenet forum called Alt.Barney.Dinosaur.Die.Die.Die Instead, the very opposite was stated by Derek in the episode "Playing It Safe" (he said that they're not only people you don't know, but that "they could be bad people."), which led to a short Too Smart for Strangers moral using a play of Little Red Riding Hood and a song (in traditional Barney fashion) to reinforce the message.
The Cast Showoff: The earlier cast displayed a range of talents. Min in particular did not miss an opportunity to dance, and aspired to dance professionally. Her actress actually did grow up to be a dance teacher, in addition to dancing professionally.
Dawson Casting: Some of the kids are well into their preteen years by the time they leave the show. Chip was a notable case. Luci looked a lot older than the other kids.
Of course, Luci was Tina's older sister, so it was semi-justified.
The most famous example was Jason, played by Kurt Dykhuizen. Kurt, like his character, was deaf and happened to use a hearing aid.
Claire Burdette was born a congenial amputee, much like her character Colleen.
Doing It For The Money: Possibly the reason why Barry Pearl played Professor Tinkerputt. As he mentions here: "Barney paid for my house."
It Will Never Catch On: Prior to the TV series and videos becoming hits, Barney's producers were faced with this exact trope on a number of occasions.
Connecticut Public Television executives felt this way when they couldn't see the series' appeal after watching a Barney video. After they showed the video to kids and saw their reactions, however, the tides turned and CPTV immediately got a TV contract for the Barney series.
Song writers Lory Lazarus and Stephen Baltes, who wrote songs for the initial three Barney & The Backyard Gang videos, were told by friends to leave the company for this reason. They came back to write for Barney & Friends' third season, once the character's popularity took off.
Keep Circulating the Tapes: Most of the Barney episodes and videos produced prior to 2001 have yet to receive a DVD release in North America, with a few exceptions such as "Imagination Island." Sprout reran some episodes from the show's first three seasons from 2007 up until 2010, but most episodes haven't been aired since 2000 or so. Time Life released a majority of the show's first season on VHS (with four more videos released by Lyons), but the tapes are becoming more rare.
Both the 10th and 20th anniversaries of the Barney franchise led to the video specials "Sing and Dance with Barney" and "The Best of Barney," respectively. The former even brought back a few Barney alumni to join the (then) new child cast for a "sing along."
The one hundredth episode of Barney and Friends is more lighthearted than usual, and Old King Cole comes over to party.
The duck umbrellas used in the "Six Little Ducks" number in "The Backyard Show" would re-appear in the video "Rock with Barney" along with the TV series episode "Down on Barney's Farm," both featuring the song.
Outfits from previous episodes are occasionally reused. For instance, in "Are We There Yet?," one of the items at Carlos' Cleaners is Luci's cheerleading uniform from "Carnival of Numbers".
Sleeper Hit: The original three Barney & The Backyard Gang videos are considered this. The videos didn't take off until Sheryl Leach and her team marketed Barney at a grassroots level, giving videos to Dallas preschools for free along with lists of where the Barney videos were sold.
Throw It In: Barney's voice actors occasionally ad lib various lines. Usually it's hard to hear, but when you hear them, hilarity ensues.
In "Barney's Great Adventure" during the climax scene while they are on an airplane, Barney goes from screaming in fear to complementing the balloons in a matter of seconds.
Barney: "WHOA, WHOA, AHHH- oh, nice balloons, SCUSE ME, SORRY, LOOK OUT, SORRY, AHHHHHH-hi, how ya doin?"
The Barney suit was originally going to be somewhat more "realistic" looking, with scales, claws, pointed teeth, and even lacrimal ridges. Through the various drafts, the creative team told costume designer Irene Corey that the costume would be too frightening for kids, until it came to what would become Barney's eventual design. Proof: 
What Could Have Been: Twinken , the koala-like Dream-Maker that hatches from the egg, was not in the original drafts of Barney's Great Adventure. The egg instead contained a lost baby bird. Barney was to return the bird to its mother, while uniting the kids' families as well.
Of all people, TREY PARKER (yes, thatTreyParker!) was offered to direct. One can only dream of what that would have been like.
BJ and Baby Bop were going to be more prominent in the film, mainly in scenes with the farmhouse attic. These scenes were cut due to, in the words of the director, "being too expensive."