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.
Roxas: I was partnered up with No. XIV for today's mission. Xion wore a hood the whole time and wouldn't say a word to me. Come to think of it, I didn't have a whole lot to say, either. Afterwards I went and had ice cream by myself."
Roxas: "I went up to the clock tower to have ice cream, but nobody else showed up."
Roxas: "After I finished my mission I wanted all three of us to have Ice cream, but I couldn't find Xion."
Roxas: "My job today was to help Axel find Xion. It turns out she had gone missing, but we managed to find her. We finally got to all have ice cream together, which was nice."
Roxas: The other members have been teaching me more about how to fight and stuff. It's going, I guess. Every day after work, I've been meeting Axel at the clock tower to have ice cream. It really is salty! But still sweet, too. How come it tastes so familiar?
Roxas: Axel and I went to Twilight Town today. He taught me a lot. Before we RTC'd (Returned To the Castle) we swung by the clock tower and had ice cream. Axel called it the "icing on the cake" after a successful mission. Well, except there was no cake—just the ice cream. I don't know what to write in this thing!
Roxas: Me and Axel went on a mission to Twilight Town. Afterwards, we went and had ice cream again up on the clock tower. He said friends do stuff like that. Or they laugh together. So does that mean me and him are friends?
Roxas: Today was my third day with Xion. I've gotten to know a little more about her. That's right—she's a girl, with black hair, and she can use the Keyblade just like me! I took her out for ice cream afterwards, but I'm saving the WINNER stick. Axel deserves a reward when he gets back. Xion wants to have ice cream with us from now on. Maybe we'll be friends.
Author's Saving Throw: The Ho Yay between Axel and Roxas was dripping after Kingdom Hearts II, and it helped that unlike Sora and Riku, neither of them has a "canon" love interest. The introduction of Xion and the very heavyhanded Ship Tease with her and Roxas could thus be considered this.
With Xion's true nature being questionable about her real gender, if having a specific one at all (especially amongst all the switcheroos depending on who it is sees her)...and that technically both Xion and Roxas are inside Sora and are Sora, it leaves open whether that was actually the intention.
Axel and Roxas' interactions are also written to be less Ho Yay heavy, Accidental Innuendo aside. Axel sincerely comes off as a big brother figure to Roxas rather than the "psycho ex-boyfriend" of Kingdom Hearts II, and he even flat-out says that the love he and Roxas share as friends is different than romantic love like Belle and the Beast share.
Base Breaker/Broken Base: The "Sue" status of Xion has been a source of great debate amongst fandom. It's generally divided into two camps: one sees her as a sympathetic deconstruction of a sue who experiences a short, painful, and traumatic life before finding out she's expected to kill her best friend and possible love interest, and the other sees her as a retcon-added Black Hole Sue/Sympathetic Sue who motivates the actions of the main characters more than she should have in a forceful or contrived way that wasn't needed when there were other means available, and whose increasingly sad existence is there simply to garner her as much sympathy as possible from both the characters and the audience. Or so it stands. It's controversial enough that you'll get differing opinions on a lot of things.
Roxas:No! Xion... Who else will I have ice cream with?
This nearly ruined the biggest Tear Jerker in the game. Although for some it was the line itself, and for others the line was fine but it was the delivery.
Now, in the defense of that line, no one seems to know or care that it's pretty obviously metaphorical. In this case, ice cream stands in for their friendship, which is meant to be rather pathetic and sad, as eating ice cream is pretty much all they ever did. The narm seems to stem from the immediate context (but, y'know, ignoring the overall plot) combined with Memetic Mutation.
The final fight with Xion is meant to be a tragic fight between two friends. It's a little bit hard to feel moved while Xion is constantly yelling generic taunts.
The Infernal Engine, OH GODS The Infernal Engine...
The Ruler of the Sky.
That One Level: There are many missions that are just plain frustrating to go through.
Tear Jerker: Xion's death. Wait! Roxas's capture. Screw it! The entirety of the ending.
For the former, just one line. Who else will I have ice cream with? It's honestly a shame that the line itself is such utterNarm, because the delivery is incredibly well done and sad.
Roxas's final diary entry. "I am DONE WITH THIS."
For the HD remake, almost every damn cutscene is getting full voice acting. This will most likely include Roxas and Axel's fight before Roxas leaves. As in, you get to hear Roxas and Axel, formerly best buds, screaming at each other with hatred and misunderstanding. Not to mention Roxas's angsty soliloquies. Tissues please, and it hasn't even happened yet.
That scene is included, and it is ridiculously depressing.
They Wasted a Perfectly Good Plot: For some, for a game setting before Kingdom Hearts II, it fails to provide more informations about the Organization that we already knew. We still don't know much about the members outside Axel, Saix and the six founders. Riku and Diz investigations about their enemies is also nearly ignored, and Mickey's journey is completely ignored. Many felt that Xion centered the plot heavily around her.
Tier-Induced Scrappy: Xigbar. Despite being funny, having a cool weapon (and a cool scar), being quite possibly the best partner in story mode, and having some of the best lines in the game, he's not very good for soloing in Mission Mode, and is usually only picked by people who think he's cool. But he's alright in a group when you have someone else tanking.
Uncanny Valley: While it won't mean that much to someone new to the games, it is invoked when Xion removes her hood and reveals herself to have Sora's face and is speaking with her voice, it really feels unsettling.
Woolseyism: Near the end of the game, when Roxas looks at Xion and sees Sora's face, Xion uses Japanese Pronouns to indicate that she still thinks of herself as female. The line was restructured into the third person ("This puppet will have to play her part") to get the same point across in translation.