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: Hate isn't the right word, but Conrad is considered boring to many Western fans for being the "perfect guy who completely understands Yuuri". It's this dedication that is rather fatherly that turns people off (when it comes to pairings, as Conrad/Yuuri is significantly more popular with Japanese fans than Western ones). See the Values Dissonance page for more details.
Anvilicious: The writing isn't exactly subtle when conveying the important themes of this show, what with Yuuri's constant monologues about how love is always the answer and you have to love everybody everywhere and never stop, ever! Although between Yuuri maturing into this role (which is honestly more about 'understanding and accepting everybody' than 'loving' them, although his vocabulary is noticeably influenced by his mother), the fact that the narrative allows many dissidents to be rounded characters who have good points counterbalances this rather. We are not forced to believe Gwendal is being unreasonable in preparing for war all the time, or that Conrad's willingness to sacrifice anything and anyone for Yuuri is not a potentially valid alternate morality.
Badass Decay: Saralegui starts off as cool and diabolical, and by the end of the series is... a little childish.
Complete Monster: King Belar has already crossed the Moral Event Horizon before he met Yuuri. Him constantly trying to kill him has put him in this category and the number of instances where he deliberately tries to break him just because he's a demon. He's willing to sacrifice his own people just to test out the box that is said to bring the destruction on the world if only to get rid of all demons.
To make matters worse, he took children from his own country as hostages in order to lure Yuuri out in the open knowing he would try to save them. When things get out of hands, he leaves the kids for dead. It's enough to cause most of his country to pull a Heel-Face Turn given that a human was shown to be dark hearted and cruel yet it was the demons that saved them.
Creator's Pet: Saralegui is accused of being one especially by the shippers given that he's introduced in season 3 and takes the spotlight away from Yuuri's other companions as well as being set up with the most Ship Tease in that season despite the development that happened in the previous two seasons.
Not as frequent as other fandoms but Saralegui gets a lot of flak from any other person that prefers Yuuri with someone else (mainly Yuuri/Wolfram fans). After all his previously built-up relationships with other guys never cracking his Transparent Closet, Yuuri suddenly crushes on Sara for shallow reasons.
Conrad also frequently gets the Ron the Death Eater treatment from the more militant Yuuri/Wolfram fans.
The Scrappy: Saralegui is not well liked in the fandom for many reasons.
1. He starts out as a pretty good villain (or at least Anti-Villain) but goes through Badass Decay to the point that people thought his character was wasted.
2. His character design turns a lot of people off especially since Yuuri who has been claiming to like girls the entire series suddenly develops a crush on him if only because of his feminine appearance, which makes Yuuri look shallow.
3. He gets in the way of all the pairings involving Yuuri. Especially jarring because he's introduced in season 3 and gets the most Ship Tease with Yuuri effectively pushing the other characters like Wolfram or Conrad out of the picture making shippers declare that he's a Creator's Pet.
Seasonal Rot: The third season was met with a pretty lukewarm fan reception, compared to the first two.
Ship-to-Ship Combat: Several, but Yuuri/Wolfram vs. Conrad/Yuuri is probably the biggest one. Or Yuuri/Wolfram vs. any other Yuuri pairing, as is often the case in the English-language fandom.