All of the meddling with Superboy, but most notably the edict to purge Superman from Legion lore after they went out of their way to pull a saving throw to preserve the status quo via the Pocket Universe.
Naked Legion — Mike Grell's run as artist for the series, thanks to the infamously skimpy costumes he drew the characters in.
The Archie Legion — The post-Zero Hour reboot Legion, both because of the return to the "idealistic" end of the Sliding Scale of Idealism Versus Cynicism following the Darker and Edgier "Five Years Later" version that had gone before, and because of the artwork of Jeff Moy, the Legionnaires artist for the first run of the reboot.
Another nickname given to them is "Melrose Legion", due to the fact that Jeff Moy's versions of the female Legion members resembled the actresses on Melrose Place, not to mention the fact that quite a few '94 Legion storylines evolved around who was dating who...
Sneckie — The '94 reboot version of Princess Projectra ("Jeckie" for short), thus nicknamed because, unlike the preboot and threeboot versions, the postboot character was a giant snake.
Fakefire: The nickname given to fans who loathed '94 Reboot version of Wildfire due to the significant differences in his origins.
Jarth — Following Garth "Live Wire" Ranzz's Heroic Sacrifice in the postboot Legion Lost limited series, the character was brought back inhabiting the crystalline body of his former teammate Jan "Element Lad" Arrah.
Also see the character sheet for the most common terms used to refer to the different versions of Legion continuity.
Promoted Fanboy: Several examples of this throughout the series's history, including one of the earliest examples from The Silver Age of Comic Books: Jim Shooter, a teenaged fan of the series in the 1960s, wrote to the editors of Adventure Comics, arguing that the adult writers were doing a fairly poor job of capturing authentic teenage dialogue and characterization. In response, they let Shooter take over writing duties, and he produced some of the best-remembered stories in the team's history. It also served as his launching pad into the American comic book industry: he later went on to serve as editor-in-chief of rival Marvel Comics, and eventually returned to the Legion in the 2000s in a run that was cut short by Executive Meddling.
Also true of Tom and Mary Bierbaum, who were regular fixtures in several Legion of Super-Heroes fanzines in the 1980s before taking over writing duties in 1989, first alongside Keith Giffen, and then on their own. This led to some significant problems with Continuity Porn, Flanderization, and a lot of Ascended Fanon.
Jim Shooter began submitting stories and layouts to DC in 1966 at the age of thirteen, after following the series as a fan. He returned to begin writing for the Threeboot incarnation of the Legion at the end of 2007.
The TMK run was infamous for sounding like overwrought fanfic elevated to canon. Because it was, in a manner of speaking (though whether or not it was actually overwrought depends on the observer): Tom and Mary Bierbaum (the "TM" in "TMK") were active participants in the Legion of Super-Heroes APA scene in the 1980s, and many of the ideas they introduced when they were writing the title were originally conceived in those pages.