On Sesame Street everyone is your friend. That's kinda the point. And he wasn't trying to guilt trip Swedish Chef, he's a child who's oblivious to things outside his frame of reference. Besides, we can assume that Big Bird has no idea where meat comes from besides "the supermarket."
Angst? What Angst?: Ma Bear is surprisingly not too upset over canceling her vacation plans to accommodate for the Muppets beyond the fact that she wasted three months taking surfing lessons. Possibly aided by the arrival of a blizzard, which probably would have stranded her at the airport.
Big-Lipped Alligator Moment: Kermit and Robin's visit to Fraggle Rock qualifies. The special kind of stops to make it happen, especially because it happens right at the height of the "Miss Piggy lost in the blizzard" plotline. Robin is exploring the cellar and finds a Fraggle Hole; Kermit and Robin go inside and meet the main Fraggle group; they all sing a song about giving gifts; Kermit and Robin leave. The Fraggles do briefly show up again during the carol singing finale, but they don't have any lines and just observe the action, so it feels more like the creative team wanted an excuse to bring in the final major Jim Henson property to complete the crossover.
Continuity Lockout: Anyone from an area with its own localized human segments of Fraggle Rock was probably confused by the appearance of Doc as Sprocket's owner. Even some U.S. viewers who didn't have HBO, couldn't get CBC, and hadn't watched the animated version of Fraggle Rock (which was airing on NBC at that time), were locked out. (And remember this was before online streaming, or before you could just Google who they were.)
Keep Circulating the Tapes: This special has notoriously never been officially released in full (due to copyright issues over some of the songs) and remains unavailable on Disney+. However, fans have managed to distribute it and it remains popular despite this.
Memetic Mutation: At least in the Muppet fandom, virtually every line is quotable.
"Careful of the icy patch!"
"The dog is not the turkey! The turkey's the turkey, you turkey!"
"We'd love to see your act!" "In fact, we'd hate to miss your act!" "In fact, we'd love to hate your act!"
Nightmare Fuel: Though it's thankfully a short-lived idea, the concept of the Swedish Chef killing and cooking Big Bird as the centerpiece of Christmas dinner. While that sort of subject matter isn't totally out of the ordinary for the cartoonish, slightly more mature Muppets, putting a character from the Lighter and Softer Sesame Street crowd in mortal danger makes the joke pretty dark.
Jim Henson's brief cameo at the end. We miss you, Jim...
Not to mention seeing Richard Hunt's main Muppet characters together (as he succumbed to HIV in 1992) and, later, all the numerous roles played by Jerry Nelson, who passed away in 2012. There's also the passing of writer Jerry Juhl in 2005 and Caroll Spinney in 2019.
To a lesser extent, Elmo's appearance in the Muppet crowd at the end (Kevin Clash is still very much alive as of this writing, but he was forced to resign from the character due to abuse allegations in 2012). Likewise Steve Whitmire's characters (Sprocket, Wembley, Rizzo, the Turkey, etc., not to mention Kermit and Ernie, which he would take over after Henson's passing), as he was let go from the Muppets in 2016, although he is also still very much alive.
Along with all of the above, Doc's whole role in the special becomes bittersweet after Gerry Parkes' 2014 passing.
Of course, seeing all the Muppets together like this is a happy tearjerker.
Big Bird and Swedish Chef singing "The Christmas Song (Chestnuts Roasting on an Open Fire)", which even brings the Chef to tears. All the more so after Carroll Spinney's passing in 2019.
Kermit worrying about Miss Piggy in the snowstorm is also considered heart-wrenching.
