Above the Influence: Despite the persistent efforts of The Children (and Kyosuke, and Fujiko, and the entire free world...).
Badass Normal: subverted in the pilot chapter where he's (although completely oblivious of it) a level 7 anti anti ESP-er link... which still makes him a normal guy... but in the serialized manga (and anime) he is just a Normal.
Freudian Excuse: Averted. Despite some horrific treatment at Suma's hands, a prejudice, as well as a childhood of being feared by her family, Kaoru is a kind hearted person. Even as a villain, her stated goal is protecting ESPers rather than hatred of the human race. Still, it's lucky she met Minamoto when she did.
Wife Husbandry: Unlike Minamoto he is trying to invoke this trope, but it's backfiring badly. And by badly, we mean hilariously.
An Esper brainwashed by Black Phantom
Bad Future: It looks like he's in for this. In a recent chapter, Feather shows Minamoto a vision of the future. In said vision, Bullet dies (or at least is critically wounded) after getting in the way of a trap set up for Aoi.
Anti-Villain: Kaoru sees him as such, though Kyosuke is always zigzagging across the Moral Event Horizon. Regardless, his intentions are at least understandable, and he is providing a home and support network for the espers that BABEL isn't able to find or help.
Freudian Excuse: The reason he's so distrusting of normals, Minamoto in particular, is because his commander when working in the Japanese military had come off as a very reasonable kind man who wanted nothing more than coexistence between espers and normals, but then tried to murder Hyoubu and made it clear that his ideal world was one in which humans control espers. Because of him, Hyoubu has trouble bringing himself to trust normals who work towards coexistence between espers and normals.
Psychopathic Manchild — In Volume 6, he does avenge a young girl who is severely wounded in a suicide bombing - but only because the bomber ruined the good mood brought on by the flowers she sold himand because she looks astonishingly like Kaoru. Later, he says to the leader of the terrorist group (before he blows up the plane they're on):
Kyousuke: I go anywhere my interest leads me. I do anything I want to. I kill anyone I don't like. That is all.
Reality Warper: Between his highly-refined telekinesis and hypnosis, Kyosuke can do just about anything.
Well-Intentioned Extremist: While PANDRA's main goal seems to be making sure that espers win the war between normals and espers, should it ever come, but it's implied that he'd be perfectly fine with a world in which humans and espers can coexist peacefully. The problem is he doesn't think that it's possible. Also, PANDRA's actions rarely ever directly harm civilians, espers and normals alike.
Teleporters and Transporters: Her teleportation allows her to teleport only a part instead of the whole like the others. The parts are still connected and if they are too far apart or too far away from Mio, they will reattach on one side.
Punch Clock Villain: Magi treats PANDRA like it's a job: objectives are set, paperwork is organized and you put in overtime to get the big projects done on time. All this makes him more dangerous than the rank and file who treat PANDRA like a hobby or a game.
Ship Tease: With Momiji, who decides very early on that he's marriage material. More so when the only time we see Magi lose his cool is when she gets hurt.
Team Dad: The one who gets stuck trying to establish rules and discipline. Also had to raise at least three ESPers. He's more detached and stern than Minamoto, but given that he works for Kyosuke that's something of a necessity.
The Dog Bites Back: Being always mocked for his hobbies by Sakaki makes it that much easier for him to join PANDRA for good; he nearly murders Sakaki in the process.
In the anime, BABEL really had it coming when Kaoru blackmailed him into building an anatomically-correct Oboro doll for her, then just left him holding the bag when it was discovered, causing him to lose out on his chance to take his girl out.
Freudian Excuse: His coworkers' general disdain for his hobby gives him another reason to spy on them for PANDRA.
No Name Given: He's always referred to as "Black Phantom", "Boss", "Father", etc.
Battle Butler: A notable aversion: despite the way he dresses and his loyalty to Black Phantom, he lacks Psychic Powers or other combat abilities.
Phantom Daughter/Yuri Kumoi/Mirage/Phantom
One of The Children's classmates. Actually Black Phantom's daughter, a Hypno user with a split personality. The Yuri personality knows nothing about Black Phantom and has no special abilities; Mirage, who considers herself the main personality, created her to fool Psychometers.
Power Trio: Mirage is the superego, Yuri is the ego, and Phantom is the id.
Split Personality Merge: currently, in the manga, Yûri's locked memories have awakened from the major's lockdown. As a result, all of her previous personnalities have merged under 'Yûri Kimoi' as the dominant one. She has since decided to erase her existence from the Children's memories to pursue a personnal vendetta against Black Phantom.
A mysterious, very powerful Esper whose mind can be transferred between bodies using raremetal quartz. She has amnesia, but has a vague idea that her goal is to "change the future". In love with Minamoto (even more so than everyone else). Originally implied to be Kaoru from the future, she's actually an amalgamation of the memories of all 3 children (and possibly others as well) from the future, with Kaoru as the nexus.