Angst? What Angst?: Monstress of the Postboot continuity. Her backstory reveals that she was the Spoiled Sweet daughter of an industrialist on Xanthu, and was shocked to see him swat away a worker during a tour of one of his factories. She went to help the worker and discovered that he had with him a gene bomb that went off and mutated her into her current state. After that, her father no longer had time for her and she was shunned by both sides of Xanthian society. Despite all that she is still quite cheerful and pleasant to be with, and her hope for the future and a happy ending were never squashed. This might make her a Stepford Smiler, except she never denies or pretends that something isn't wrong.
Legion fans were not exactly happy to learn that after the New 52 Legion title was cancelled in 2013, it would be replaced by a completely unrelated Justice League of America title called Justice League 3000. (Regardless of the fact that the creative team behind the book was intended to be Keith Giffen, J.M. DeMatteis, and Kevin Maguire, the alumni behind Justice League International.) Notoriety for Justice League 3000 picked up after artist Kevin Maguire was fired off the book before it even went to print, for unrevealed reasons (Maguire took to Twitter and insinuated that the book's editors wanted something "dark and gritty", which really makes you wonder why they hired the team behind JLI).
From the Retroboot, there was the presence of Earth-Man in the Legion. The guy, introduced by Johns, tainted the legacy of Superman to spite the Legion because he felt rejected by the Legion. and instead of channeling that into something positive like the Subs, resorted to gathering up a bunch of Earth's other rejects and created a new wave of Fantastic Racism on Earth... this man is now a Legionairre... and was chosen to be Green Lantern... While many like his character arc, it's not hard to see how many others wouldn't exactly want to read about this guy being in the Legion.
Monstress. There are those who found her to be annoying She-Hulk rip-off, and those who found her pleasant and an awesome character.
The first reboot Wildfire and Sensor, both were radically changed from their original counterparts to the point of outright alienating fans of said characters.
There was some degree of grumbling about Shikari, whom fans interpreted as a reinvention of the preboot character Dawnstar. The complaints weren't quite as loud as they had been with Sensor, though, possibly since, beyond having similar powers, Shikari was more distinct from Dawnstar than Sensor was from Projectra.
The 5YL Legion. Was it merely elevated fanfic, pulling needless retcons in order to let the writers insert their pet theories into the Legion's history, and pointlessly trying to be darker and edgier or was it a mature development for the Legion? Generally, it's the former, but there are still some die-hard fans.
The Reboot Legion. Everyone seems to agree that the reboot itself was completely necessary, given the clusterfuck of continuity that was the Legion post-Crisis, which only got worse with the 5YL Legion. However...
Regarding the Legion itself, some found them to be too kind-friendly and lighthearted. Others like this approach, and noted that that's how the original Legion started, and that focusing on the group as teens first made for better characterisation.
The early issues. Some think the series rushed too fast into bringing in new members and retelling old stories. Others like the new, more diverse cast and found the retellings interesting enough to be warranted.
Olivier Coipel's art got a mixed reception from longtime Legion fans, as, for the time, it was a much more modern look than the mostly traditional artists the Legion usually gets, with some deriding his scratchy art. Others liked his kinetic art style, and thought he modernised the Legion a bit. Noticeably, he is a much more universally acclaimed artist these days, with a much cleaner style.
Was it a pointless reboot filled with mean-spirited jabs at older people (many of whom make up the Legion's fanbase), or a mature, original look at the Legion concept? Noticeably, there seems to be an overlap between fans of the Reboot Legion and Threeboot detractors, though Preboot fans are known to also make their dislike pretty clear. With years since their last appearance, their standing has fallen significantly.
The Jim Shooter run. Was it a nasty, mean-spirited, unpleasant run of stories, filled with a surprisingly large amount of sexism? Or a So Okay, It's Average, more traditional Legion run where Shooter did his best with the Threeboot team and editorial interference at the time? Generally, people praise Francis Manapul's art, however, though not to the degree of his post-Legion work.
The Retroboot: Some thought of the team as existing purely on the Author Appeal of Geoff Johns and cashing in on nostalgia, making several unnecessary jabs at the other Legions, while not getting the spirit of older stories. Others appreciate seeing the original Legion again, especially as a more traditional approach while the Threeboot were doing their own thing.
Complete Monster: Silver Age foe The Controller wasn't one to let morality get in the way of his plans for universal conquest. Abandoning his highly advanced race, The Controller decided to use his superweapon, the Sun-Eater, to obliterate every inhabited system in the Milky Way, starting with Earth's sun, Sol. When Ferro Lad's Heroic Sacrifice destroyed the Sun-Eater, The Controller attempted to brainwash the Legion into becoming his new army, then sought to murder them all when that plan failed. Convinced of his own innate superiority, and willing to wipe out an inhabited galaxy just to send the a message, The Controller would let nothing stand in his path of becoming the universe's Dimension Lord.
Gates' first appearance was as part of a Failed Draftees Montage; he was brought back to join the team, and became a popular member.
XS and Kinetix are two of the most popular Postboot characters, to the point that any fan who wants a sketch of the latter will get one from Jeff Moy.
Wildfire; brought back from the dead (originally was supposed to have been a one-shot character) twice due to fan response (the second time, the first issue after the writers who dropped a bridge on him left the book).
Also Shvaughn Erin, Dawnstar, Dream Girl, V4 Matter-Eater Lad and Shrinking Violet.
Harsher in Hindsight: In the Johnsboot/Retroboot rendition of the Legion, the Science Police had become vastly xenophobic thanks to the influence of Earth-Man and the Justice League. When Lightning Lad showed up in the 21st Century and discovered the crime scene with Karate Kid and Una's dead bodies, he immediately starts attacking the police. After he's calmed down, Garth tells Batman he doesn't like cops, especially human ones, from past experience. Given the very disturbing rise in police shooting deaths in the last couple of years, Garth's contempt for the police becomes much more understandable.
Cera Kesh, an applicant who tried out for the SW 6 Legionnaires and got called a "cow" and "porker" by Live Wire and Inferno. Inferno also made fun of the few zits on Cera's face. This humiliation is what led to Cera being picked by the Emerald Eye of Ekron as its new Empress.
In her first appearance, Eyeful Ethel was very pretty (with the exception of the multiple eyes around her head). After she got older she become rather dumpy, and her extra eyes were now permanently on her forehead. Following the reboot, she lost weight and dyed her hair.
Saturn Girl's Threeboot counterpart, along with Threeboot Invisible Kid. Francis Manapul redesigned her as being somewhat "hippy" with a little more weight then the other girl Legionnaire, but she is in no way fat or chubby. One of the complaints she has about herself is that people consider her "dumpy". Ultra Boy, in an attempt to make her feel better while she's in a rut with Lightning Lad, says "you're sexy for a dumpy chick".
Lyle Norg, in the Threeboot continuity. Francis Manapul made it a point to design Lyle as a bit round and less of a typical skinny kid. This is averted when other artists pencilled issues during Jim Shooter's run, but in the issues that Manapul did illustrate, after the Legion gets new uniforms, one can note that Lyle's belly sticks out a bit.
I Am Not Shazam: Many people operate under the belief that Glorith was another of the Time Trapper's identities. The truth is, that she merely replaced him as the Legion's time manipulating Big Bad. All his accomplishments became her's, and she remembered everything from the previous timelines. She even met the Trapper in the remains of his pocket universe and tried to stomp out his remaining consciousness while gloating how everything he created was now her's, only, as she put it, "better".
It Was His Sled: Darkseid's status as the main villain of the Great Darkness Saga. Despite the reveal only happening at the end of the penultimate issue of the story, it's pretty much widely known amongst comic fans and is the big selling point towards getting people to read the storyline. The image of the entire Legion bowing to him on the final cover of the arc has become so iconic that any compilation of the saga will have Darkseid's face on the cover. For reference the oversized hardcover has Darkseid on the front cover, him on the back cover, "kneel before Darkseid" in big bold letters on the back cover, and he's imprinted in silver on the actual trade itself.
Lori Morning wasn't very liked by fans, as she was a bratty Tagalong Kid that lacked powers, only being able to use her H-dial to morph into random superheroes. The fact that the creative team intended to be a younger version of the villainess Glorith didn't help matters. Putting her on a bus was one of the first things to occur once a new creative team took over.
The 1994 reboot versions of Princess Projectra and Wildfire got this due to their radically different origins. The later never recovered though the former did garner a level of popularity.
Tyroc, the first black character to join the Legion: He was an angry black man-type character whose backstory implied that the 30th century was actually that racially segregrated, with him and others living on an extra-dimensional island. His superpower was to even warp reality by screaming. Mike Grell had intentionally given him a ridiculous costume, as he hadn't liked the concept of the character. After the original Legion continuity became prominent once again, Tyroc was returned to the team, with his controversial origin never mentioned and a less ridiculous new costume, to the relief of many.
Post-Zero Hour Princess Projectra was actually a giant snake who used her illusion powers to pass as human in the issue she joined, until she revealed the surprise. An Author's Saving Throw was set up but never pulled off, where she became a pink naga after being exposed to a biological weapon designed to cause instant evolution towards it's victims, with the option of turning her fully human if fans rejected the new look. Unfortunately, the second reboot canceled that incarnation of the Legion, and the plot device never triggered.
Projectra was first subject to a (somewhat) shocking swerve in the 1980s when she was dragged out of retirement by Paul Levitz when he unmasked Sensor Girl. Sensor Girl was originally supposed to beSupergirl, who in an "out" to keep her around after her death in Crisis on Infinite Earths, would be running around with the Legion with a mask on, using her Kryptonian super-senses as her main super-power.
More overtly was the fact that Kinetix was supposed to become the '94 Legion's version of the Emerald Empress, having turned evil after losing her powers and being forced off the team. But the positive fan response to the character, plus their realizing where the plotline was probably going, led to the swerve where fan favorite Shrinking Violet turned out to have the Emerald Eye instead.
In the 5YL continuity, it's revealed that Lightning Lad had been dead since early in the Legion's history, and that Proty (who was thought to have sacrificed himself to bring Garth Back from the Dead) had either been using his shapeshifting powers to impersonate him all these years, or had had accidentally committed Grand Theft Me with Garth's corpse (it's not entirely clear which from the single story in which this was revealed). And had married Saturn Girl, and had two kids with her. The fans did not rejoice, and the revelation was essentially ignored thereafter.
Issue 17 of the post-Flashpoint series has quickly established that things are going to get very bad for the Legion. It opens with the reveal that Sun Boy is dead after getting his skull crashed piloting a crashed ship to save his teammates from dying, and to add insult to injury his body is eaten by the natives of the planet the ship crashed on, cooked and picked clean down to the bones. The whole issue seems to be starting off an arc that is going to have similar ramifications as the "Magic Wars" story.
They Wasted a Perfectly Good Plot: In the story transitioning from the Reboot to Threeboot Legion, when the reboot Legion is cut off from the timestream, Shikari is thrown clear and ends up on Earth in the Threeboot timeline. Shikari never shows up in the Threeboot LSH book, and nothing is ever done with this plot thread until Infinite Crisis, when the Reboot world (Earth-247) is shown among the worlds Alexander Luthor is manipulating... and Shikari is suddenly back with her team, with a reaction amounting to "Oh, there you guys are." Particularly irritating since Shikari's race has an inborn pathfinding ability which has previously been shown to be able to direct teleportation through interdimensional space...
Lighning Lad's been brainwashed, killed, lost an arm, had his brother go insane, you name it. He isn't known as "the unluckiest Legionnaire" for nothing. The first reboot made it even worse: Saturn Girl and Cosmic Boy don't even pretend to hide their sexual tension and Saturn Girl shamelessly shuns Garth to spend just about all of her free time with Cosmic Boy