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.
Broken Base: The beard and hook hand. Some prefer the clean cut look, while others prefer his bearded, Viking/pirate look.
Complete Monster: Black Manta makes his living as a brutal pirate who is hell bent on destroying Aquaman at all costs. To this end, Manta once killed Aquaman's infant son by trapping him in a chamber that suffocated the boy, despite Arthur's best efforts to save him. Manta continues to torment his nemesis by targeting and murdering those he can. Not even Manta's own family is exempt from his cruelty: his own son, the new Aqualad, was the target of Manta's wrath when Manta attempted to murder him with zealous hatred, for no other reason than rejecting the path Manta wanted for him. Manta is a vicious, hateful murderer who would poison the entire oceans just for a chance to hurt his nemesis.
Epileptic Trees: Secret Origins #2 has Dr. Shin state that the reason for Arthur's Super Strength is due to his mixed heritage. However, Orm is shown to be of equal strength, but is said to be the son of Atlanna and the then-Captain of the Atlantean Guard. While this could be because Jeff Parker wrote that expanded origin story while Geoff Johns wrote their fight, it could also mean that one of Orm's parents is human. Meaning Atlanna either had an affair with another human after being married, or that she isn't Orm's mother, meaning Orm isn't royalty.
Ensemble Dark Horse: Arthur could count as one for the New 52, specifically for how mature he's written to be. In an age where other characters like Batman and Superman are being aged down so that they are hip with the kids, to the point that their continuities barely make sense in Bruce's case, Arthur is written as a mature adult who is married in all-but name, and has taken on barely any Darker and Edgier traits. His relationship with Mera, a stable, adult relationship, has also been praised.
Orm's New 52 incarnation is pretty popular, if only because it made him an Anti-Villain and gave him depth, with his relationship with Arthur growing beyond simple Green-Eyed Monster. He got the Sinestro treatment in that Johns turned him into a much more sympathetic and interesting character, and many readers are waiting for his return.
During the 2000s run in an Ostrander Aquaman was described by several people. Each one described him in a different way: an even grittier version of the Scraggy Bearded Barbarian of the '90s; the old, clean cut Aquaman of the '60s with an extended Aquafamily; a powerful humanoid composed of water and as a perfect lover.
In-universe Black Manta likes bring up the fact that he murdered Aquaman's infant son.
In-universe Aquaman and Mera enjoy some sort of "floating reputation", being both described as useless mockery of heroes or as powerful beings on their own. See Memetic Badass and Memetic Mutation.
My Real Daddy: Phil Jimenez has this reputation in regards to Garth, since he was the one who gave him the Tempest name and power upgrade.
Geoff Johns seems to be acquiring some of this now thanks to his successful relaunch of the character in the New 52.
Nightmare Fuel: The Trench. When you realize that we still have no idea just what lives in the bottom of the ocean, there's an equal chance that those things may or may not be real.
The Problem with Licensed Games: "Aquaman: Battle for Atlantis" is universally considered one of the worst videogames ever created. So bad it even inspired its own special category for awful video games on gaming show X-Play: The "Golden Mullet Award."
His resurrection in Brightest Day has resulted in him saving children from pirates with Mera by summoning undead sea monsters. So perhaps getting rescued again.
The Smallville version even got a pilot for a live action television spin-off after the numbers for the fifth season revealed that his debut episode was the most watched episode of the season.
The first issue of the recent Aquaman reboot seems to have this as its goal: it mostly involves Aquaman being badass and addresses a lot of common misconceptions about him. Four issues in it seems to have worked. Aquaman is being praised as one of the best series DC has, and Aquaman himself has gotten a big boost in appreciation without using more badass aspects like the harpoon hand and beard.