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.
Angst? What Angst? - Rather than complain about their problems, characters on both sides use their angst as motivation to beat the crap out of their opponents.
Ginta sorta subverts this in a few scenes where he does feel genuinely homesick; but he quickly gets in over his head enough that he really doesn't have time to angst.
Ginta sort of zigzags this in general after Snow is captured. Sometimes he can't get her out of his head and other times he seems to forget that she even needs rescuing. He does legitimately angst after she dies, but tries to hide it from everyone... nobody buys it.
Arc Fatigue: Pretty much everything after the sixth round. The show starts adding more and more filler and padding which prolongs both the monotonous Tournament Arc as well as Snow's rescue. Compared to the manga where she was only gone a volume and a half, she's missing 26 episodes here. It's mildly annoying watching it now, but imagine watching the show as it was airing. That's half of year of mostly filler. And then there's the Ghost Chess arc, which is loved by Yaoi Fangirls and people who wanted a better resolution to Phantom's character arc (that was anti-climatic in the manga) but disliked by others. The last 7 episodes are generally considered to end the series on a high note, though.
Base Breaker: Snow is a very divisive character to say the least. There are many who see her as a scrappy for getting in the way of Ginta and whoever they ship him with and for getting captured on screen at least twice (four times in the anime), but she does have her fans. Notably, she always ranked fairly high in the manga's character polls, always in the Top 10, frequently in the Top 5.
Ensemble Darkhorse: Alviss is by far the most popular character in the series given that almost all artwork and fanart is mainly about him. It's even lampshaded in the series by Edward and Belle.
Fanon Discontinuity - Most MAR fans, do not acknowledge MAR Omega as part of the canon-or a sequel. Mostly because, it was done by a completely differently mangaka, Ginta isn't even the main character, and the original main team characters are now basically support cast-or background characters.
Lots of people also consider the anime ending superior to the original manga's, which was anti-climactic, rushed and little bittersweet.
Jack/Snow is surprisingly more popular than Jack/Pano (if only because of the Ghost Chess arc) on forum discussions.
On the Ho Yay/Foe Yay side, you have Ginta/Alviss, Phantom/Alviss and Rolan/Alviss with the first two being nearly tied.
Basically, disregarding O Cs and self-inserts, the most popular ships seem to be Ginta X Alviss, Ginta X Phantom, Alviss X Phantom, or some combination thereof, though some might argue the Yaoi fans are an extremely vocal minority. As far as heterosexual pairings go, Ginta is almost exclusively shipped with Snow, and Dorothy is near-universally paired with Nanashi. Jack is either left alone or paired with Pano, or rare cases with Snow. Alviss is... Unsurprisingly almost never paired heterosexually, but in the rare instance he is, it's usually Belle.
Moe: Snow/Koyuki can be this at times, but there's also Aqua and Loco.
Moral Event Horizon - Halloween killing the bystanders, Peta killing the Luberian Thief Guild, Chimera turning Gido into a Tortured Monster, and Galian betraying the Thief Guild to Peta.
Diana could cross it at any number of points depending on the viewer. Keep in mind she betrayed her sister and her country and later sent the Chess Pieces to raze it, manipulated the entire world into TWO full-scale wars, and helped create the Chess Pieces in the first place, all to satisfy her greed. And that's not even taking into account how she treated poor Snow, in that she created her in the first place, having cloned her from Koyuki, which led to her real mother's death, for the purpose of sacrificing her to gain the real world as well.
Nightmare Fuel - You've gotta admit, there are some scary things in this series. For example, the character Chimera, whom, upon having her mask broken off, she is shown to have a mass of multiple eyes on the right side of her face. Also, Pinocchion, just Pinocchion.
Also Edward and Belle are annoying, clingy mascots. Edward is only there to be a handicap for Alan before the curse was undone and once that happened, Edward had no character of his own. Belle in comparison reminds too many people of a certain fairy from a certain video game due to her annoying voice.
The Untwist: Quite a few "plot twists" in this series are fairly obvious if your Genre Savvy, mainly because the foreshadowing is a little too thick. Some of these include, Ginta's dad being Danna, obvious because his father had gone missing six years ago... exactly when the last War Game happened. Koyuki and Snow being connected in some way, granted the exact nature of the connection differs between the manga and anime but nobody is pretending that the fact they were connected was in any way some kind of surprise. The Queen being Diana, and Diana being Dorothy's sister... I mean just look at her! They looked too similar for the revelation of them being related to be a surprise. The only plot twists that aren't untwists are ones that border on Shocking Swerve, such as Babbo being the spirit of the previous Caldean Elder... because nothing hinted at that earlier.
They Wasted a Perfectly Good Plot - The series started out as a perfectly respectable adventure series, and was setting up for an epic journey across the country. Then the next episode cuts to them already at their destination and the majority of the series is spent on a fighting tournament. This wouldn't be so bad if the battles weren't such a step down from those of Flame of Recca. Fortunately, the anime fixes some of these things by adding filler arcs that don't have to do with the tournament and the aftermath which included the Ghost Chest arc and the final arc which had a much more satisfying ending than the original manga.
While the ending being superior is a majority opinion to be sure, there are those who'd argue the filler detracted from the show more than it added. It could just be that it was rather misplaced as well. RescueArcs and Tournament Arcs are the two things you DON'T want to prolong.
Of course he was possessed by the Orb, the main villain of the series.
Too Cool to Live : Played with both Alan and Danna, the former is much stronger than the main cast, but a flaw in order to not make him too cool and the latter was possessed by the Big Bad, only to be revived at the end of the series, Chimera plays this straight though, only losing because Dorothy is too witty about disrupting her concentration
Villain Decay: When they were first introduced, the Chess Pieces were not only viewed as very powerful, but very menacing as well, having all kinds of people join them, battle seekers, greedy Arm collectors and even rapists. But after volume 3, they succumb to The Worf Effect to show how powerful Team Mar is, and the members are significantly qurker and/or losers who angst too much about their problems.