To a minor degree at the beginning of the run, many avoided the story simply due to the switch-up of Luna's and Celestia's roles, not helped at all by Celestia/Corona rejecting an offer of friendship when in-canon Luna accepted it, or Corona willingly threatening the lives of foals to get her way.
The Night Court and its shenanigans. More than a few people who started reading the Lunaverse stopped once the Night Court's politicking started to take over.
Author's Saving Throw: The Return of Tambelon and to a lesser extent Magic Tutor, both by RDD himself and intended to fix some problems with the Lunaverse's narrative. The former exists primarily to change Corona's character into something less monstrous and therefore both easier to write as a villain while also making sure that she won't go overboard and have people hating her return to grace by the end of the season. Zecora's role in the series is also more clearly defined she is working with Corona because she knows that Corona has some part to play come the season finale. Magic Tutor, meanwhile, exists to finish Twilight's arc happily, by placing her in Ponyville where she can make friends, while also making it clear that no one in Ponyville really cares about the Ursa Minor incident from Boast Busted, since monster attacks happen all the time in Ponyville.
Broken Base: There are four camps relating to At the Grand Galloping Gala, the culmination of the season 1 Night Court storyline. One faction feels that the fic ruins things because it makes the Night Court too dark and evil, able to cause a whole town to suffer because one pony in it hates Trixie. One faction feels that the fic ruins things because it turns Trixie and company into hypocritical criminals and Luna into a tyrant (an ironic protest given that she expressed fear of that very thing happening In-Universe) for letting them get away with what is essentially treason in order to expose/punish the (comparatively smaller) crimes of the bad nobles. A third group thinks that the fic breaks everything in both ways; that by implying that treason is the only way to fix the Court, it makes the Court far more broken and malign than before while also not actually solving the corruption (since Trixie and company would get away with what they did). And a fourth faction likes things just fine or wishes the Court's punishment had been more severe.
Pinkie Pie and Blueblood. RainbowDoubleDash has repeatedly referred to it as "the one good thing to come out of At the Grand Galloping Gala", a fact that is surprisingly universally agreed upon.
Diamond Tiara and Scootaloo also fill this role quite nicely.
Crazy Awesome: Trajectory. His ultimate plan? It's to destroy the sun with a catapult. Which basically means firing safes, anvils, and pianos towards it. Essentially, he's shooting unbelievably heavy death in every direction because he doesn't understand how far away the sun is.
As of At the Grand Galloping Gala, some readers perceived the L6 as descending to the level of the corrupt nobles and planning to commit high treason to fight them, which caused them to stop caring which side wins.
A vocal few, prior to At the Grand Galloping Gala were getting sick of the Night Court arc on the basis that it was taking up time in-story better-suited for going after Corona, and believing the political power-grabbing only muddled the whole arc.
Ensemble Darkhorse: Octavia Philharmonica has had a Character Development arc throughout the season that is arguably as meaningful as those of the Elements of Harmony, even getting her own character focus episodes.
Exiled from Continuity: As you might have noticed, some people have...issues...with the Night Court, and the direction it was taking the Lunaverse. This extends to the series creator himself. While no Night Court story has been decanonized, RainbowDoubleDash has flatly refused to allow any more canon stories focused on the Night Court.
The exception to this is TalonAndThorn's Climbing the Mountain series, for three reasons: First, it was already in-progress, and RainbowDoubleDash didn't want to cut off TalonAndThorn from finishing it; second, it is far more focused on showing a positive side to the Night Court, rather than constant scheming and dirty dealing (notably, our perspective character is the newly-created Baron Mounty Max and him learning the ropes and trying to improve things for his new province, rather than any political games focused on gaining power or gaining control of the Elements); and third, because it is considered "soft canon" that other "hard canon" fics can contradict and take priority over if need be.
Fandom Nod: Boast Busted twice hints that Lyra's hooves were turned into...something, which is always cut off before the speaker can finish. Those who are familiar with Lyra's fanon characterization can probably guess what that something is. More hints to these events are dropped during Family Matters. The events mentioned are finally shown in "Helping... Hands?", where Lyra is turned into a human directly. And, in a Mythology Gag, hates it.
In Carrot Top of the Line Rarity comments multiple time about liking Carrot Top's mane. There is also a Mythology Gag in there.
When Shining Armor meets Luna, he notices an abacus.
Silver Script's (Ditzy's boss) baseball bat has words "Love and Tolerance" written into it.
In The Hero of Oaton, Cut N' Dry starts crushing hard on Raindrops at first sight.
Kindle and his thing with Raindrops, which she returned up until she learned who he was.
Cheerilee makes passes at Corona every time they meet, albeit only because Corona tends to be reduced to sputtering and shock (that a common pony would make a pass at an alicorn like that) by them rather than out of any real feelings for her.
Hype Backlash: Antithesis, the villain of the long-awaited Crisis on Two Lunaverses has been derided for her lackluster nature.
Symphony For The Moon And Sun, while generally considered to be good (to say nothing of being A Day in the Limelight for Octavia), the plot still requires that Luna never bothered explaining what her deal was with the song, or even forbidding it from being performed at all, or maybe checking to see whether Octavia had actually wanted to play it in the first place.
Old Friends has Cheerilee's old friend Notary come to town to inform Cheer that once, while they were very drunk, the two got married and now she wants an annulment. Even though she doesn't want the marriage either, Cheerilee decides to run away, resulting in a Looney Tunes-esque chase about town when all Cheerilee has to do is sign the annulment and Notary would leave.
Iron Woobie: Piano Amour. Her family's situation was going downhill so hard that she didn't care anymore even if she'd fail the symphony: she'd get Luna's attention one way or another, no matter what it'd cost to herself.
Jerkass Woobie: If you still think of Applejack as being a jerk after reading Carrot Top Season, you might be part demon. Everything she does she does because she thinks that she has to and, since she works too hard, she has no idea why the townsfolk might not like her.
Diamond Tiara in Scootalong for the Cheer.
Arguably, Corona herself.
Misaimed Fandom: Some readers have a habit of assuming the worst of certain characters. The standout examples being the belief that L!Applebloom is a bully similar to Diamond Tiara, and that L!Twilight would be perfectly willing to team up with Corona. These ideas annoy RainbowDoubleDash enough to discourage people from believing them. Both of these examples lessened considerably after Carrot Top Season and A Chance Encounter were published. The former showed Applebloom in more detail and the latter proved that Twilight does not sympathize with Corona.
RainbowDoubleDash has also noted that readers have come to see the Lunaverse as a lot darker than he originally intended.
Up to Eleven with At the Grand Galloping Gala, which even has some of the authors protesting how dark the story has gotten.
Corona kidnapping about 50 foals from Ponyville and threatening to slaughter them unless Ponyville stays nice and quiet and accepts her as their new Queen. This is maybe ten minutes, max, after she's escaped from the sun.
Later, Corona decides to destroy Canterlot and a good chunk of the surrounding countryside due to Shining Armor's trolling her, despite stating not thirty seconds previously that, as an immortal, she has all the time in the world to wait for Shining Armor to grow tired and stop being able to project his shield around Canterlot. She is fortunately (if accidentally) stopped by Zecora before she can go through with it, but still...
The reader consensus is that Flim and Flam have well and truly crossed this horizon by kidnapping Apple Bloom.
Long comment threads in 'At the Grand Galloping Gala' reveal that some folks think that fic included moral event horizons for Viceroy Night Light (who delayed reconstruction funding to Ponyville because he hates Trixie), the Court as a whole (who tolerates this), and/or Trixie (who RainbowDoubleDash implied would use the Truth is a Scourge potion on the entire Court and force them all to reveal all their secrets, which would be hypocritical, since that act itself is highly illegal and borders on treason but she intends to do it to protest the illegal dealings of the Court).
Given she's a corrupt, scheming, greedy ass long before we meet her, it's hard to tell when Puissance actually crossed the line, but a good contender in Ice Hearts is threatening to forcibly separate Ditzy and Dinky, even claiming to spoil (read: effectively brainwash) Dinky so hard she'd forget her mother.
Narm: The amount of times Ditzy refers to Dinky as "my little muffin" through Ice Hearts is excessive.
Never Live It Down: Applejack's early portrayal as dangerously obsessive over her farm's future, to say nothing of her becoming increasingly hostile and paranoid through Carrot Top Season.
The early portrayal of the regular Mane 6 in general was (and on occasion still is) this.
One-Scene Wonder: Coconut, Featherbed, Marching Order, Duke Greengrass in Carrot Top Season, and the Sirens (with a musical number, no less)
Ron the Death Eater: Some feel the way the canon Mane Six (particularly Twilight and Applejack) were written falls into this, due to the treatment they get and how few good points they seem to have.
On the other hand, the various authors of the Lunaverse noticed this problem and have spent considerable time rectifying their original portrayals of the Mane-6 in later fics.
Tastes Like Diabetes: Cherilee's reaction to learning that Dinky saved for almost a year to get money for Ditzy's birthday present.
Also lampshaded later by Amethyst Star.
Word of God: The authors of the Lunaverse are fond of putting in additional details or tidbits in the comments sections or author's notes of their stories. For example, the official hierarchy of Equestrian gentry and nobility was outlined in the comments of Longest Night, Longest Day, rather than directly stated in any story.