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.
And the simple fact that by the end there was a sense of been there, done that, with the antics of Lina and the gang - especially the antics of Lina - just not being as funny as they would've been in the two previous seasons.
Crack Ship: Xellos/Inspector Wizer Freion, because of their bizarrely chummy interactions in the Slayers Revolution anime.
Creator's Pet: Lina and Naga for the light novel writer and artist, Lina even moreso for Rui Araizumi, the light novel artist - most of his artwork is of her, and most of his newer pieces (and art in the Slayers Smash novels) have her either in sensual poses or with prominent nipples. It's also been made clear in-universe that both of them, Lina moreso, are abnormally powerful compared to most mages.
Die for Our Ship: The worst of it has died out (and despite the constant Ship Tease, the Lina/Gourry and Amelia/Zelgadis pairings have been laid pretty thick since NEXT) over the years, but there's still a good deal of bashing of Amelia having feelings for Zelgadis, with fans finding her either too stupid, too weak, or obnoxious and spoiled (which she is far from), finding that the intelligent Zelgadis deserves the equally as intelligent Lina. In a similar vein, fans also wanted Gourry to not be with Lina for similar reasons.
On the other hand, fans who did prefer Lina/Gourry loathed Gourry/Sylphiel, with a lot of venom.
Then, of course, there's the ever-popular Yaoi choice of Zelgadis/Xellos, with the alleged justification that they secretly love one another, despite the blatant hatred Zelgadis has for the latter.
Filia is only allowed to be with Xellos, not anyone else, especially Valgaav. Because their constant bickering and passive-aggressive treatment of one another is clearly the sign of a loving old married couple. Never mind the fact that Xellos is completely incapable of feeling positive human emotions, while Filia is a part of a bigoted race of god-worshiping dragons.
Epileptic Trees: Some fans theorize that the reason Lina's so powerful is because she contains one of the seven fragments of Ruby-Eye Shabranigdo and is unconsciously drawing power from it. After all she's really good at casting Dragon Slave, which calls upon Ruby-Eye's power.
Fanon: less so than some series, but fairly well-entrenched. Among other things, fanon claims that Xellos's boss, the Mazoku Lord Beastmaster Zelas Metallium, is a good friend and drinking buddy of Luna Inverse... despite the fact that Luna Inverse is (Good Is Not Nice aside) a very powerful Paladin who houses a fragment of the chief god of the Slayers world in her soul, which means the two are natural enemies.
KanzakaDex claims it's because of one misinterpreted picture (it's Luna and Dilgear, not Zelas).
There's also the theory that Zelas drove Dolphin insane and that they hate each other (Also false: when they show up briefly in the novels, they are on good terms and she's no more crazy than Zelas).
Foe Yay: A flashback in season four of the anime shows Rezo putting a hand on human!Zel's cheek, making him do a Luminescent Blush.
Growing the Beard: In regards to the anime, the first season can seem rather directionless, with the humor and pacing kind of awkward for most of the first half, not helped by a rather mediocre English dubbing if you're watching that. By the time Amelia is introduced though, the show starts finding its groove. On top of that, the English dub gets better halfway through the season when Veronica Taylor and Crispin Freeman join the cast and really give Zel and Amelia their voices. It also starts off a more interesting plot and introduces cooler villains, like Zangulus and Vrumugun, who continue to chase the heroes so even the filler episodes don't feel so pointless. By NEXT, the show really finds its stride, reaching its signature level of humor and solidifying the characters' personalities and quirks, as well as having what is arguably the best plot and character development in the whole franchise.
Hilarious in Hindsight: Lina was once the postergirl for "flat-chested". Compared to many many characters today, she is quite ample.
That pickpocket Lina forces to give her massages? Hellmaster himself! She should add that to her list of things to brag about.
Jerkass Woobie: Zelgadis and some of the villains, particularly Eris and Duclis.
Memetic Badass: Lina Inverse manages to play this straight and subvert it at the same time. Whenever she deliberately tries to use her reputation to her advantage, nobody recognizes her... but that's because she uses nicknames and titles that she created herself to feed her ego. Mention any of the dozens of names that stem from her bad attitude and misbehavior, such as Dragon Spooker, Bandit Killer, or Enemy Of All Who Live, and people will run for miles, as everyone seems to have heard of them. Considering that, in the fourth season of the anime, this is someone who was put on trial for the crime of being herself, and that even her friends couldn't come up with an adequate defense, that does explain things.
Moe Moe: While pretty active and go-getting, Amelia is the youngest of the four main cast members, also has the larger chest of the two girls, tends to be the cutest, and as noted below is sometimes used as a punching bag by the villains so that viewers will feel intensely protective of her. The term came into being some time after Slayers aired, but Amelia seems to have been a prototype of the trope alongside characters like Rei Ayanami.
Narm: Sylphiel's voice acting in the first season of the dub. Particularly her Big "NO!" when she sees Syraag's destruction at the hands of Rezo.
The Scrappy: Sylphiel's demure personality, strength in healing magic over attack spells, and feelings for Gourry made her heavily disliked by a lot of Western fans who have the Real Women Never Wear Dresses mindset. Because of that, the more stubborn Filia is preferred by them. On the other hand, both Sylphiel and Filia are only moderately liked by Japanese fans, and Hajime Kanzaka, the novel writer, dislikes Filia (and Slayers TRY in general).
While Naga is highly popular in Japan, there's a divide of people who like her elsewhere, probably due to the Slayers Special novels not being exported. Despite her sheer sex appeal, many find her laugh to be obnoxious and overused, or can't stand how airheaded she gets.
Prince Pokota never gets a lot of love, from any kind of fan, probably due to his high magical power, angsty past, and Leeroy Jenkins-like attitude.
Squick: In the first season, Zelgadis claims that Rezo the Red Priest is both his grandfather and his great-grandfather. Word of God has since been passed on that this was a verbal mishap, and that not only was Zelgadis supposed to be unsure whether Rezo is two generations removed (grandfather) or three (great-grandfather), but he's truly Rezo's great-grandson.
Another mistranslation in NEXT has Amelia referring to both Christopher and Alfred as her uncles. Christopher is Phil's brother, so that works. However, Alfred is Christopher's son, and looks to be about Amelia's age, which makes Amelia and Christopher cousins. This botch is also probably the reason that Alfred sounds so much older than he is in the dub.
Viewer Gender Confusion: If you watched NEXT in Japanese without subtitles, you'd have a hard time determining exactly what gender Hellmaster Fibrizo is. The dub fixes this by giving him a boy's voice.
The Woobie: Your hometown gets destroyed twice, and your main love interest doesn't even notice your affections, only to have him fall in love with the main heroine when the world is at stake. And even then it's not like they at least stay together and are happy. Isn't it sad, Sylphiel?
Amelia is also somewhat Woobified as noted above; you're supposed to feel terrible for her and give her a protective hug when a villain tears a great bloody hole in her back or tries to rip out her soul or what have you. Amelia herself, though, is too damn genki to be held back by any of this.