Bizarro Episode: The special is this, mostly, in the larger context of the Star Wars canon. Also to George Lucas and other cast members, who do their best to pretend this never happened. On the bright side, though, it's not canon anymore since Disney's ruling on the Expanded Universe.
The animated segment served as the introduction of Boba Fett, the biggest ensemble darkhorse of Star Wars in general. So much, in fact, that despite Lucasfilm wanting to forget about the special, the cartoon found its way onto one of the Blu-Ray bonus discs as an Easter Egg.
Fanon Discontinuity: If there's one thing all fans and creators of Star Wars can agree on, it's that this thing never fucking happened. Of all the things that Lucas himself declared non-canon, well before The Walt Disney Company purchased Lucasfilm, Holiday Special was the only one that didn't contradict the Original Trilogynote Technically it was listed as "Secondary canon", which despite the name was the fourth level of canonicity, as low as you could go without being outright non-canon. "Secondary canon" is to be "used or ignored as suits the author". Basically the Holiday Special was adopted as canon by way of Broad Strokes, where Luke, Han, and Leia all came to visit Chewie's family on Life Day, but they most certainly did not take part in a crappy variety show as they did so!. It was also very deliberately excluded from the Disney canon despite George Lucas directing part of it.
From one of the commercials in the New York City recording: "Fighting the frizzies at 11."
Boba Fett's continuous use of "friend".
The whole special is memetic in how awful it is. George Lucas's seething hatred of it is also rather memetic.
Misblamed: Some fans blame George Lucas for the quality of this, but in reality he had very little involvement due to filming The Empire Strikes Back at the time. In fact, Lucas had one of his trusted former USC classmates installed as the initial director in order to make sure that the special would be at least somewhat faithful to the original film. Unfortunately, Lucas' favored director quit after disagreements with the producers and CBS replaced him with the guy that would go on to produce Pee-Wee's Playhouse. The results speak for themselves. According to writer Bruce Vilanch, however, the idea of the special focusing on Chewie's family, and not including subtitles, was all on Lucas. According to Pat Proft, Lucas signed off on everything, which is believable due to Lucas being a Control Freak.
Narm: The whole thing, but special mention must be given to the actor cameos and the attempt at "warmhearted" holiday cheer at the end: Han, Luke, C-3P0 and Chewie are supposed to be moved by Leia's song of hope, but look stoned/bored out of their minds. Considering that Carrie Fisher was whacked off her skull on drugs while making this special, they probably were.
While the premise was as silly as the rest of it, Bea Arthur's performance as the cantina owner is actually a bit moving. Sadly, it doesn't save the rest of the thing's horribleness.
The animated segment as a whole - looking at you, Boba Fett.
The random stormtrooper who fights Han and (due to the way the scene is shot) apparently trips over his own gunnote though it also appears he could have tripped over a few logs next to his feet after being disarmed by Han's weak karate chop, thus nailing a perfect Railing Kill. The Wilhelm Scream he makes is the cherry on the parfait.
Padding: One theory is that the special was originally to be one hour, but the network wanted to sell more advertising, so they insisted that it be expanded to two hours. That would explain some of the more ludicrous scenes.
Squick: Elderly Wookiee Itchy looks like he's masturbating to holographic alien porn, which is completely wrong and disgusting no matter how far away your galaxy is. He's also watching it in the middle of his living room, in front of his daughter-in-law and grandson. Worse yet, this is apparently a common enough occurrence that they don't even bother commenting on it. Even worse... this is exactly how the writers and producer wanted it to come across. Merry Christmas, children! And they would have made it more explicit if not for one of the few necessary instances of Executive Meddling.
They Wasted a Perfectly Good Character: Ackmena, Bea Arthur's character, is actually considered to be the most interesting character created for the special. However, she doesn't appear for very long.
Took the Bad Film Seriously: Bea Arthur, alone among all the big-name guest stars. To her credit, she's talented enough to elevate her sequence into something watchable and almost poignant. She was also no stranger to 1970s variety shows, so she knew how to adapt her Deadpan Snarker Mode to the role. Her own comment on the special years later was that she hadn't been keeping up with Star Wars and its massive cultural impact at the time, thinking of the gig as just singing a musical number to "a bunch of people with funny heads."
Han Solo's cartoon representation. He almost looks like Mick Jagger. Melting Mick Jagger to be exact.
Mark Hamill was still recovering from a car accident that required extensive facial surgery, so he ends up a rare live-action human actor example. The make-up needed to cover his scars made him look like a Ken Doll.
The Woobie: Krelman, Harvey Korman's character in the cantina scene. Yes, he's a bit weird with his head hole, but he's so sincere and so lonely, he evokes sympathy almost accidentally. Cantina barmaid Ackmena and her customers as a whole also fit the bill.