Madrigal for a Nostalgic Afternoon - Another musical form we haven't seen in the Symphonies before, a madrigal is a song, usually unaccompanied, for several voices, usually short and always intended to evoke an emotional response (madrigals are often, but not always, love songs).
In this case, Avatar Storytime was cut from Goodbye and Hello, As Always mostly for length, and because it wasn't finished when the rest of the movement was ready anyway. Fortunately, since it has a consistent theme throughout the scene, it can work as a stand-alone side story - and has a couple of nice callouts for bits of The Legacy of Korra into the bargain.
 the one with the hair - Adult ancient Rohan was specifically designed to greatly resemble his father Tenzin to facilitate this joke. That said, Rohan was remarkably well-appointed in the hair department right after he was born.
 photos scanned - A risk in any society transitioning to digital, I'm afraid... *looks glumly at his instamatic photos from young adulthood, college, and high school.*
 nearly square - Meant to imply that this shot was taken with Dìqiú's rough equivalent of a Kodak Brownie Hawkeye camera, which made 2¼" x 2¼" frames.
 arctic camel - Like a regular camel, but much more furry. We did not make them up, they exist in the show.
 I hope! - Now you know why the White Lotus guards looked so skeptical when Korra wanted to go for a ride outside the compound in the first episode of Book 1.
 I am killed - Attentive readers may recognize the blocking in this scene, which was inspired by a similarly adorable moment in How to Train Your Dragon 2.
 built like a linebacker - Tonraq's design was in fact based on the linebacker father of a female MMA fighter who was one of the inspirations for Korra's design. So it all fits!
 to oil my scales - A common kink among the scaly dragons.
 a late summer afternoon - This image is in the Legend of Korra, Book 1 artbook, top half of page 140.
 that's her scooter - Minami has a large collection of her great-great-grandmother's things, having made it something of an avocation to track down those that passed out of the family's possession between their lifetimes and reacquire them if the present owners are willing to deal. So far, the scooter has eluded her.
 Professor Protester - The Equalist Protester from Book 1 never got an official name, so we decided that Korra would always have called him this anyway, even after he went legit and got a real job as a (very abrasive) poli sci professor at RCU. Korra was not a poli sci major, but had to take a couple of his courses while working on her Government & Public Admin MA.
 turned my Senna into an adventurer - The image of Korra's mother becoming a racing driver, aviatrix, and general worldwide shooter of trouble in middle age was originally sparked by my entering her name into the wrong website search and looking it up on Wikipedia instead of the Avatar Wiki. If you do the latter, you get the Avatar Wiki's page on her; if you do the former, you get a disambig, the top entry on which is the page for the late Ayrton Senna (1960-1994), three-time Formula One World Champion. That led to the thought of the first photo, of Asami letting her drive a racing car, and that, in turn, unpacked into the whole "Korra's not the only globetrotting adventuress in the family" concept, which tickled me so much I had to run with it.
 Crescent Island - Crescent Island has long been a nexus of Fire Sage activity, and frequently Avatars would go there to train and get closer to the primal fire (as it was set on a semi-active volcano). After the latest destruction of the Fire Temple there (in 100 ASC by a Roku-influenced Aang), the Veil Nexus was discovered by the Sages during the recovery efforts after the War ended.
 through the looking-glass - Since official contact with Zipang had not yet been established, Asami is probably not quoting the title of Lewis Carroll's 1871 sequel to Alice's Adventures in Wonderland. This is most likely a translation artifact to do with what she actually said, which at this stage would have been in Tongyu and presumably referred to some similarly-themed local folk legend.
 pigchicken - Pigchickens (or pickens) actually do exist in the Avatar world. As do pigcows (moo-sows), wooly pigs (pigsheep) and pigroosters (pigsters). There are also pig deer, which look like pigs but have antlers and fur.
 Future Industries: Still Alive - What later became known to Standard-speakers as the V-model Satomobile (the company's first all-new car design under Asami's leadership) was a triumph. I'm making a note here: "Huge success."
 distant metal towers - These are in fact the skyscrapers of Zaofu, an Earth Kingdom city New Team Avatar gets to visit in Book 3.
 United Republic Space Agency logo -
 kept reporting the Equalist attack - The attack happened in the Legend of Korra Book 1 episode "And the Winner Is", and in the episode we do see one of them shock the pro-bending announcer in the course of events. According to a note in the Book 1 artbook, a planned scene in which he got back up and kept talking was cut from the episode for time, but at least in the UF version of history, it did happen.
 The Crimson Lizard and the Case of the Criminal Councilman - A Film By Iris de Chateaubriand. Very loosely based on Korra's first case, as transposed to the retrofuturistic city where all the Crimson Lizard films are set (which is really not much of a reach from the actual Republic City; indeed, many Dìqiú fans of the other Crimson Lizard films, not knowing the larger backstory from Koji Aho's novels, assume they are set in Republic City).
An excerpt from the Republic City Tribune's positive, but often baffled, review of the film:
The great thing about this mover is that it presents the only conceivable way the Equalist Uprising could've been any crazier: if Amon's chief lieutenant had really been an international jewel thief playing all the other parties involved off against each other in order to make a giGANtic score.
As of the spring of 2410, Criminal Councilman has evidently not been released in the "big universe" market, or Corwin would have seen it.
Karana and Azana's graduation - It should be noted that at the time this piece was started, during Goodbye and Hello, the long history of Karana and Azana had not been even finalized yet.
postcard panorama - Niri's in this photo too, the white speck wayyyy up at the top of the observation gallery.
 the South Pole's greatest photobomber - Each of Korra's polar bear dogs has had at least one specialty...
 it doesn't work across the Veil - Skuld, of course, would fix this in the next full movement, Familiar Spirits.
 Raava -
The pattern on Korra's Lens is based on the upper part of Raava's spirit markings (her "face"), while the ribbed construction of its wristband echoes the lower part.