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.
Americans Hate Tingle/Germans Love David Hasselhoff: Touma is much less popular in the west because he's seen as arrogant and unlikeable, and the fact that his false betrayal would have gotten Agumon killed were it not for The Power of Friendship, as well as the fact that the entire cast just overlooked this detail was the last straw for many western viewers. Masaru is also surprisingly popular for being one of the most unique Digimon main characters in the history of the franchise.
Broken Base: Fans are split on how good this series was. Those who think it's good either love it or like it just fine. Those who think it's bad despise it.
Complete Monster: The cowardly, bespectacledscientist, Akihiro Kurata, is the single most despicable human being to appear in the franchise. Planning on committing genocide on Digimon due to nothing more than a petty grudge while conquering the world, Kurata created the Gizumon that would kill Digimon and stop their natural reincarnation cycle, which he first unleashed upon a noble Digimon who had been a surrogate father to the boy Ikuto. Kurata's reaction to Ikuto sobbing over his father's loss was cruel, hysterical laughter. Kurata then created a weapon to kill thousands of Digimon in a single blast and blackmailed one of the humans into working for him by threatening to murder his sick sister, before experimenting on said sister. Kurata's hatred extended to awakening a monstrous demon and attempting to merge with it to obliterate everything he saw as an enemy.
At least in the original, Lalamon gets a little too touchy when Ivan says he will become Yoshino's boyfriend. Then again, it's hand waved as Lalamon playing along Ivan as an excuse to distract him from commanding the Gizumon, but she does get some suggestive lines like "Don't worry, I won't hand you over that easily".
Then there's Touma's battle with Nanami. Touma seems to really ignore the half-naked Nanamis in favour of the powers even he cannot calculate (read: Masaru). As much as he doesn't get over being ignored because Masaru is today's designated saviour, that particular scene fired up the bipolar sensors.
ManyMonster of the Week Digimon were good guys in previous series. A lot of people were rather unhappy with seeing so many of their old favorites shoot at the good guys for a few minutes and then die. Examples include Digmon, Garurumon, Togemon, Garudamon and Zudomon.
Hilarious in Hindsight: The main characters' Digimons who can evolve to Mega-level are color-coded in orange, blue, pink, purple, and red; the same color as those of the main characters of DokiDoki! Precure. Only with the color for The Heroine and The Chick switched. It doesn't help that both series are written by the same person, Ryota Yamaguchi. And it doesn't help that both series have a Tag Along Kid character who is voiced by Rie Kugimiya, either.
Idiot Plot: Hashiba gives Kurata his support despite working with Satsuma and Yushima, who can both confirm that the man has open issues with authority, questionable mental stability and was responsible for compromising the original rescue mission in the Digital World. The whole Japanese Government takes this beyond reason by hand control of the entire military to a Kurata, even after he had committed an open act of terrorism by personally bombing DATS headquarters.
In addition, the final story arc introduces Yggdrasil/King Drasil and the Royal Knights, immensely powerful super-beings whose combat abilities rival those of Burst Mode Digimon, and in some cases even surpass them entirely. So where were they during Kurata's rampage throughout the rest of the season?
Jerkass Woobie: Nanami and Ivan of the Bio-Hybrids. Nanami when solemnly monologuing about how she's been lonely all her life due to being socially isolated because of her intellect, and Ivan when it's revealed that he only works for Kurata because he needs the money to support his many little brothers and sisters, and is too dim-witted to truly realize what he's doing is wrong.
Love to Hate: Fans sometimes praise the series for having a villain who is genuinely despicable and hateful, not least of all because watching him get his just desserts is so satisfying.
Memetic Badass: Masaru. As the fandom put it, "MOTHERFUCKER PUNCHES MEGA-LEVEL DIGIMONS IN THE FACE".
Mis-blamed: No, Ikuto's Tarzan-speak was not added to the english dub. He spoke broken Japanese in the original version too.
Moral Event Horizon: Kurata crossed this at lightning-speed when he returns to the Digital World and engages in a brutal massacre.
Nausea Fuel: A great many things count, but most especially Kurata's head coming out of Belphemon's body.
See "Funny Aneurysm" Moment, but many returning Digimon who fared less well in Savers than in previous series got this reaction. Piyomon/Biyomon arguably has it the worst, not least of all because the director made him male, subjected him to The Worf Effect, and made him much larger. Had he been another species, the fans would probably have viewed him as The Woobie, not hated him.
Unfortunate Character Design: The Savers redesign of Yatagaramon suffers from this. He has a white mane that really stands out thanks to his mostly black and purple design. Said mane is braided into a single rope that dangles freely with a bell to each side of it. Guess we should call the Savers version the four legged crow.
Within the franchise itself. Previous Digimon series had firmly established that humans should not put themselves in the path of an angry Digimon, especially if it's large enough to cause serious harm to you. In Savers however, Masaru can only put himself in danger. Agumon can't evolve without him risking life and limb.
Also the fact that DATS is essentially in the business of doing the same thing that was considered "evil" when Hypnos did it in Digimon Tamers. And yet they're our protagonists.
Though arguably, the Hypnos/DATS thing is justified, as Hypnos killed Digimon outright, while DATS only sentenced them to another reincarnation.
The Woobie: There are at least three: Keenan, due to his tragic backstory and conflicting feelings over his own human-Digimon identity; Thomas, due to his family struggles and the loss of his mother; and Yoshino, who suffered from a severe childhood-rooted inferiority complex for the first third of the series.
Woolseyism: Masaru/Marcus makes a pun on Thomas/Touma's name when they first meet and calls him "Tonma" (This means something along the line of "Stupid" or "Fool"). Because it's a Japanese pun, it doesn't translate well...however another nice pun works, too. In the English Dub, Marcus/Masaru calls him "Nerdstein", a pun on his last name. Doesn't have exactly the same meaning as the Japanese pun..but instead keeps the bit about Masaru making fun of Touma.
Also Citramon, a fruit-based knockoff of Nanimon, who was a BomberNanimon in Japan. Doubles as being Bowdlerized, since a gruff and hairy male chucking bombs to destroy large structures for no reason reads "terrorist" to a lot of people.