It wasn't really clear beforehand that this was a separate-story episode... but in the sense that it, and the dreamlike framing device, allowed more freedom for lunacy, that did allow also for sillier fun. Bart's story was OK - Lisa's also (her tree complaint, both in the dream and more so in real life, was really odd though) - Marge's, with Martha Stewart giving sinister advice, was a nice concept, and would have overstayed the joke except that the execution was still pretty funny. And then... uh, take that, Sesame Street? (OK, I'll admit to a bit of a thing for Katy, especially in an even racier dress than the Elmo bit.) Actually, that wasn't just loose but a whole 'nother format, and was pretty chuckle-worthy if not hilarious.
DYN: ...the "tasteless gifts for dad" department is a (Christmas Story) leg lamp in a wooden crate (also as in the movie)? ...Richard and Lewis as appropriately silent elves? ...among other icons, the Abominable Snow Monster (Rankin-Bass Rudolph) in Santa's workshop? ...Lisa has (giant) elf ears? ...Homer's magazine in the Martha Stewart story is "Modern Fart Denier", and "denier" (pronounced another way) is a word she is bound to be familiar with? ...the Katy Perry bit is probably inspired in part by the Sesame Street controversy, but it's modeled more after The Muppet Show? (see below) ...but at least the hand puppet Simpsons look a lot better than the full-body costumes they trot out from time to time? (also, hand-drawn family pictures on the walls?) ...the "39 days of Christmas" cuts away just as they get to the 12 days we already know (but it was 12 lords a-leaping, which in my experience has been part of a nonstandard ordering)? ...and Katy keeps talking as the Gracie logo starts, but ends with the word "stop" where the "shh" would be? (I'm not sure if that or the "denier" thing was intentional.)
Previous episode stuff 8F02: Holiday-specific fantasies framed by family members dreaming (see also below) JABF04: Bart mentions he was naughty but hasn't (for example) gotten anybody pregnant 3G04: Homer as a (female) pinup model
Other stuff If you didn't see it, the end of Lisa's dream seems to be inspired by Inglourious Basterds. The theater assassination attempt is pretty close, especially with the lighting of nitrate films, and possibly Marge's terrible German (though that comes from another character).
The last act, with the "Fluppet"-inspired puppet show, has got to be because of the Katy/Elmo thing that was apparently too cleavage-y to go on Sesame Street. (I'm on the fence about that, incidentally.) I thought it was a little too soon to have been written that way from the start, and it probably was... but the puppet show is much quicker to produce than full animation, and I would not be surprised if it began as a three-story episode (note that despite the new 4-act format TOH XX and XXI were still three stories), and the rest (and intro, see below) were trimmed to fit this in. Or, potentially, an entirely different fourth story was planned and cut.
Finally, did you notice no opening sequence at all? Not just not a normal one, but not an abnormal one. The action just started. This could have been because of the final story, as noted above. The only previous episodes not to have even the created/developed by credits as part of an opening sequence (but instead put in with the rest) are 7G08, 7G05, 7G11, 7F04, and 8F02. (The first was also a Christmas episode! The next two were from very short open season 1 episodes, and the last were the first Treehouses of Horror.) Even the shortened JABF07 didn't do that.
In fact, the name of the show didn't show up either (I guess until the copyright screen). The only episodes I recall that happening in before were JABF15 (Ullman short) and MABF12 (the Ke$ha opening). Maybe JABF14 ("24 Minutes")? Possibly also the shortened JABF07 ("Springfield Up") and the "Bartman"-enhanced repeat of LABF05. Any others?