Arc Fatigue: The Mine Arc, where the crew is trying to repair the Gekko, which ranges from roughly Episodes 15-20. Most of the episodes include a lot of Angst on the parts of Renton and Eureka and Holland's abusive behavior towards Renton reaches its upper limits. Fortunately, the Charles and Ray Arc begins almost directly after, which is where the series begins to pick up in steam again, which it manages to maintain for the remainder of the plot.
Author's Saving Throw: A huge point of criticism is the climactic moment near the end of the series where Renton reunites with his father in the library of the Scub... because Adroc doesn't say a damn thing. No explanation for what he did and why he did it, just a few wordless glances. All this... because the casting unit couldn't figure out who to select as a proper voice for Adroc because none of them sounded manly enough. As a result, a mountain of emotional tension and mysterious background goes unresolved from our point of view. Thirteen years later, the Hi-Evolution reboot trilogy comes into development and this time, straight from the previews, we see Adroc actually has a voice and the voice actor is a perfect fit, and Adroc is key to a major flashback that is potentially compatible to the original series timeline.
Talho. Some find her irritating, which was not helped by her actions in episode 4 where she worked Renton like a housemaid and punished him for a financial outcome he had no control over. However, some give her slack for being the only member of the Gekkostate who is willing to call Holland out on his Jerk Ass behavior.
Renton himself. Viewers will either see him as The Woobie and a likable, engaging lead character, or a Wangsty brat who surpasses Shinji Ikari in being a depressive wuss who has no business being in the line of work he's in.
Dewey. Many see him as he was intended, a Hate Sink with ambition up the wazoo that gets scores of innocents killed for stupid reasons, himself included. However, with the dark developments in sequel Eureka Seven: AO, Dewey's actions in hindsight look far more like those of a Well-Intentioned Extremist... but still unforgivable nonetheless.
Broken Base: Fan reaction to Hi-Evolution 1 has been sketchy. There are a lot of people upset to see some characters cut from the apparent reboot and some steep changes that mess with the original story, and many who were salty when it became known that only around the first 30 minutes of the film and the last few minutes were new animation and material and the rest was just a repackaging of the original series around the second season. As for Hi-Evolution 2, people are wondering what in the world is going on with the story because the promos are darting in all different directions and suggesting a new universe, the old one, the reboot, and a weird soccer match between the mecha across all the various series incarnations.
Charles and Ray are present for a single arc about mid-stream of the series but they get a lot of fan love for treating Renton with respect (they all but adopt him), and for being extremely sympathetic Anti Villains. Some wish Renton stayed with them, mostly due to how much of pricks the people at the Gekko could be towards him.
Moondoggie is one of the more minor members of Gecko State but he has a lot of fans. Part of this is for his attractive design, and partially for his growth and character development.
The trio of girls who show up to Axel's workshop and can be seen in Renton's class; their designs are unusually well thought out, even for background characters. If only we knew their names.
Everyone Is Jesus in Purgatory: Played with in the soccer episode. Norb says they should play soccer and several people ponder why they're playing soccer. At the end, Norb says something along the lines of "If you had fun, that's good. If you learned something, that's good too."
Growing the Beard: Starts off inauspicious and mean-spirited, starts picking up once the Beams are introduced, picks up even more after Episode 26, and explodes several episodes later.
Even though (or perhaps because) the movie takes place in an Alternate Universe, many fans refuse to acknowledge the movie's existence. Previously popular characters like Dominick and Anemone getting bridges dropped on them or just plain not showing up, and throwing out some of the themes that defined the original series were also factors that contributed to fans refusing to accept the film.
Just to illustrate the level of rejection, a common nickname for the movie in the Russian fandom is literally "The pocket full of shit", mocking its Japanese title "The Pocket Full Of Rainbows".
The Hi-Evolution film trilogy being another Alternate Continuity, instead of what was thought to be a Compressed Adaptation with new scenes that still follow the canon of the original series, has killed some fans' excitement for it. The second film of the bunch seems to have a mixed reaction with fans wondering if they should even try to make sense of the timelines anymore because the promos are all over the place and somehow the film includes all the franchise's mecha... in a soccer match.
It actually turned out to be much worse, with the 2nd movie revealing that all of the previous E7 properties including the original series, AO, the games, and Pocket Full of Rainbows are the delusions of an insane Eureka who had accidentally killed Renton, effectively meaning all the previous entries into the franchise, including the original series were basically ruled as Canon Discontinuity in one fell swoop. Naturally, the fans who found were quick to the drop the Hi-Evolution films and have low expectations for the third film.
Harsher in Hindsight: Ray's anger towards Eureka, for being sterile because of the Seven Swell, and can't have children of her own. This stings a lot more when you realize that in the sequel series, Eureka can't have children in that world without them dying, her firstborn child dies shortly after birth, and she wasn't able to raise Ao for most of his life. They were both robbed of their chances at (natural) motherhood. This is one of the reasons it's the Contested Sequel and a frequent Fanon Discontinuity.
Movie!Hap and Movie!Stoner hold down Eureka and rip her top open. What makes this worse is their apparent motivation for doing so—they were concerned about their reenactment of a myth (you know, those typically orally passed down and allegorical stories) not following the story to the letter.
In "Paradise Lost", Renton struggles with the idea of addressing Ray and Charles as his mother and father. ...anyway...
Charles:(embraces Renton, shoving his face into his own chest) "I worked up a sweat at the gym just now. Do I smell bad?" (Renton looks up at Charles and shakes his head) Charles: "This is how your dad smells." Renton:(tearfully) "It really is a good smell..."
In "Wish Upon a Star", Renton grabs a flower that (presumably symbolically? The ending is a bit strange) appears in Nirvash's cockpit. As he does, there's a "ding!" sound effect like he just picked up a video game powerup.
The Silver Box in Hi-Evolution was a musical weapon to use on the Command Cluster and looked more like a rave party than a superweapon. It also is noted a problem arose because acid jazz failed to sync and the device soon accidentally razed the planet it was meant to save. Acid jazz helped partially doom the planet.
Even the extremely silly and hammy Charles and Ray still work in context given by the time Renton meets them, he's become a fullblown Emo Teen and they're the first people to treat him kindly in years, turning the Narm into a Heartwarmer.
Never Live It Down: Okay, Holland is a total prick to Renton in the first half of the series. Some people seem to forget that he grows out of it in the latter half and claim he remains an insufferable douchebag throughout. This attitude seemingly stems from the fact quite a people would regard physically assaulting a child just once hard enough to live down. Holland attacks Renton on multiple occasions.
Older Than They Think: The iconic insert songs "Storywriter" and "Niji" were released before the show in 2002 and 1994, respectively. "Niji" was especially a hit with Japanese and European techno fans, and it being used over a decade later as the finale's Climactic Music speaks for how timeless the song is.
Those Goddamn kids. Linck in particular. They cry in almost all of their appearances, are completely spoiled, and their continual cries of "Mama!" can become straight up the Most Annoying Sound in the series. Maurice shows his Scrappy colors later on, when they're lost on Earth. "Only love me, mama! No one else!" And then Renton and Eureka just have to go and be so damn understanding about it.
Holland's general treatment of Renton during the first half of the series is downright brutal at times. The fact he uses Renton as a punching bag on multiple occasions, basically taking out his own inadequacies on a kid, is enough on its own to be loathed by many fans.
Most of the Gekkostate members get this treatment due to their cruel mistreatment of Renton.
Whenever Talho slaps Holland, you can hear the sound of cheering around the world.
Fans were also impressed when Renton gave Holland a Badass Boast on how he came back to the Gekkostate for Eureka.
Tastes Like Diabetes: The ending could cause you to go into insulin shock even if you're not diabetic.
Wangst: Renton does a lot of griping around half of the first episode because his life isn't as exciting as he would like. Stays in sight for a while before it evolves into genuine Angst and then disappears.
They Wasted a Perfectly Good Plot: When Renton finally reunites with his father, Adroc doesn't say a damn thing. This is because the Japanese voice casting crew couldn't find an actor they felt would do his character justice. Because of this, the apparent closure between Renton and his father that needed to be addressed in that episode seems to come off as weaker and inadequate, and it leaves a bitter taste in a lot of viewers' mouths.
[[spoiler:Also, from that same episode: Renton seemingly unopposed to the fact his dad and sister are remaining with the Scub Coral instead of getting them to come back to his world with them and his grandpa. There were many instances throughout the show of people whose minds were bound to the world of the Scubs and it hurt the people they left behind, so it felt like it was stating a message that leaving people to do as they pleased at the expense of their loved ones is always the right thing to do. In what universe is that even remotely forgivable?