These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Arc Fatigue: The development of Allen and the 14th Noah is suffering this as a result from the multiple breaks Hoshino is taking and because of the writers real-life issues that have caused the manga to be on hiatus since December 2012. As a result Allen has been suffering for the last four years.
In an extension of the above fatigue, some often sight that the Arc Fatigue started from the moment of the weekly-to-monthly switch for the manga; having the story arcs going for much longer periods of real-time then previously before. The fans often debate if this is because Hoshino doesn't release enough content for a monthly release, and is stuck on a weekly release mind-set, or if it's because the fans themselves can't adjust to the new schedule and can't handle the, now slow, plot advancement then when the manga was on a weekly release.
Allen isn't anywhere near as traumatized by his sucky life as one might expect.
Subverted in Marian's sidestory. There we learn that Allen spent a lot of time without wanting anything to the point Maria forced him to eat and change his clothes. Allen managed to recover but he was not himself but acting like Mana. Across the story Allen becomes aware of this when Lenalee points that he is starting to be casual rather than formal.
Subverted by Lenalee; she has a horrible past and generally acts upbeat and cheerful, but it's mostly an act; she's been harboring a deep hatred of the Order for years and is terrified of the Inspectors from Rome.
Kanda's sort of a lesser example. He's a gigantic, unrepentant a-hole,with no heart of gold underneath, which turns plenty of people off of him. However, he still ranks very high in character popularity polls, even ranking higher than the main character at least once, and has a strong female fanbase. All Girls Want Bad Boys in action?
Probably the fact that his heart grew when Allen and saved him and Alma helped to improve his popularity.
Die for Our Ship: Lenalee gets this for getting in the way of Allen/Yu. And Eliade tends to get this a lot from Krory/Miranda fans, which is ridiculous, since she dies in Krory's introductory arc.
Dude, Not Funny!: Cross is a complete dick to Allen, with Training from Hell, emotional abuse, physical abuse, abandonment, and a nasty habit of forcing a 15-year-old to pay off debts that reach upwards of tens of thousands of dollars. This is usually played for laughs.
Ensemble Darkhorse: In one character popularity poll, Kanda managed to steal the #1 position away from Allen despite having been absent for nearly three entire story arcs.
Tyki Mikk. The author admitted that Tyki exists because she wanted to draw a handsome guy. One of the Creepy Twins, Devit, is also really popular among female fans (and perhaps even Jasdero). And new character Wisely appears to have been a big hit despite only appearing in the few latest chapters.
Road has been known to invoke this as well, even with non-Lolicon fans. And don't forget Lulu Bell!
Foe Yay: Road kissed Allen and claims to love him. Though this could be more to do with the 14th than Allen. It's never explained why she was the only one he didn't kill. Though, it's probably was simply because he couldn't. We still don't even know how she can be killed after all.
Narm Charm: Jasdevi's Fusion Dance. Relatedly, the Level 4 Akuma would look outright stupid if they weren't so terrifying.
Rescued from the Scrappy Heap: Quite a few people found Miranda Lotto to be incredibly annoying during the Rewinding Town arc. Fortunately, it doesn't even take until the end of the arc for her to get a lot better.
Chaozii Han to a lot of the fans of the series, probably due to being one of the few non-bishonen male characters. His turning on Allen without question when the Order declares him an enemy didn't help matters, either.
Johnny, for his complete irrelevance despite constantly appearing (tough hopefully that may be on its way to change) and for being generally a crybaby.
Squick: Cyril is way too touchy-feely with Tyki (who may - pending canon confirmation to take this out of fanon - be his brother) and Road (his adopted daughter). Cyril loves "playing house" so much, it gives him a nosebleed. For their part, Tyki thoroughly dislikes Cyril's attentions while Road is either oblivious or doesn't care Being way older than she looks and possibly being a Shota Con might have something to do with that.
Cross Marian, who receives a head wound that would kill any human. Although they Never Found the Body...
Skinn Bolic gets killed by Kanda.
Eshii. He had Frieza as his seiyuu, beats two Bad Ass Exorcists, and forced a third to go all out, has gravity powers, and is a capable fighter. He's also the only Level Three, That doesn't get reduced to a humiliating state or beaten easily.
What an Idiot: Jasdevi could probably have ended the fight on the Ark instantly if they'd done the right thing.
Everybody in the Order. Allen is trying to help the Third Exorcists but he is stopped by Link for no legit reason. Also, he is imprisoned for not killing Alma even though Alma was nearly dead. Nobody from the Order tries rescuing Allen even though he has not been eating anything. It's sad when the antagonists were the ones who ended up helping the hero. Also, after Link is apparently killed, Allen is blamed for killing Link even though he had almost no strength but the fact he escaped proves everything. Lampshaded too. Lenalee has lots of regrets for what happened but she is not helping at all.