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.
Draco in Leather Pants: The depiction of Bandit Keith in Chapter Nine is this, specifically the fact that he appears to care about something (and a very unlikely character) other than drinking, gambling, and America.
Fashion-Victim Villain: Duke pops his collar and wears a trucker hat tilted at the "angle of optimum irony." Later, he contemplates wearing a sheer top with sparkles to a meeting.
Fridge Logic: Joey is the only one who gets tuberculosis, despite being in close contact with several other people, one of whom he shares a drink with. Never mind the fact that this story (judging by the music used and technology) takes place in 2010-2011 and medicine is a lot more advanced than it was in late 19th century France.
Ron the Death Eater: While not a hero, Duke Devlin is (usually) on Yugi's side. The story puts him not only against Yugi and friends, but against a whole political system based on a game with which canon-Duke has no problem. It's pretty clear his name is the only reason he's the villain.
"Tristan left his chair and went to inspect. On his couch was a skinny man of average height with black, red, and blond hair spiked up with blond tendrils hanging over his face. His blue tank top was speckled with debris from the ceiling and his red kilt had flown up in the fall, revealing his pyramid-patterned underwear. Being unconscious, the guy didn't seem to care much."
He was dressed even more outlandishly than the other one; he wore a green toga with a hoop skirt underneath...Yugi's cowboy boots tapped against the wood floor as he went to collect his roommate.
From Chapter Eight (full of this, as well as "what the hell, set designer?")
"Everyone put on their new hologram-emitting chest badges, headbands, and fingerless gloves and took their positions. Rhinestone-covered stars hung from the rafters in front of glittery white pyramids. Joey lounged on a couch that had been spray-painted gold, wearing a blue leopard print tunic with a pink bobbed wig. With all the reflective objects and Joey's second skin of body glitter, the downstage area seemed to be bathed in light."
"Glittering sparks shot out of holographic badges behind the two birthday hats on Joey's pectorals. Rainbows streamed from the hologram emitters on the dancers' headbands as they pranced in a circle around the stage."
WTH, Casting Agency?: Yu-Gi-Oh characters in Moulin Rouge is probably the last thing any sane person would think to write. It's made a little better by the fact that the author tried to adapt the roles to the characters' personalities and the fic mostly uses the abridged series characterization (though, in the author notes, it says they tried to blend the dub and abridged personalities).
Joey as Satine, abridged or non-abridged, is particularly baffling.