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.
Accidental Innuendo: Happens In-Universe in Fumoffu episode 8, when Tessa says she's in the "water business"; though she's obviously referring to her being a submarine captain, the term is Japanese slang for prostitution. The English version handles this by changing it to "getting wet is my business!" (which is also lampshaded as a poor choice of words by Kaname)
Tessa gets this to an extent, as fans are split between loving her for being an adorable klutz with some great moments of badass, and hating the inappropriate, borderline-stalkerish way she persues Sosuke.
The Second Raid only made things worse; the storyline kicks off with Tessa ending Sosuke's bodyguard mission, denying him permission to explain or say goodbye to his friends, and then reaming him out in a debriefing, seemingly entirely because of her jealousy towards Kaname and frustration at Sosuke's lack of response — all of which leads to Sosuke suffering a Heroic BSOD and subsequently deserting Mithril briefly.
Gauron, aka Mister Iron, is the main villain of the first season of the show. A former mercenary from Hemaljistan (Afghanistan in the light novels) Gauron was the archenemy of main character, Sosuke Sagara long before the series began. In flashback, we are shown that Gauron was responsible for killing all of Sosuke's comrades in Afghanistan. In the present day Gauron kills a KGB agent he was working for when the man argues with him. He then hijacks an airliner after killing the captain, threatens to murder all the high-school students onboard if the authorities refuse to cooperate, and kidnaps Kaname, whom he has subjected to experiments. When that plan fails, Gauron returns months later, working as a nuclear arms dealer. When Sosuke and his new team try to interfere, Gauron kills all of them except Sosuke gloating the entire time. He later hijacks the entire Tuatha De Danaan submarine, planning, again, to kidnap Kaname, and threatening to sink the entire sub. That's in Season 1. In Season 2, we find out he's the one behind the actions of Creepy TwinsYu Fan and Yu Lan, whom he sends to kill Kaname as a means of screwing with Sosuke, before blowing himself up in a final attempt at Taking You with Me. In all of his appearances, he is incredibly proud of the number of Sosuke's friends he has killed, constantly rubs it in his face, and seems to be trying to push Sosuke into killing him. A truly sick individual, Gauron is engaged in a game of psychological warfare with a sixteen year old kid, all because of a warped Stalker with a Crush obsession.
Gauron's successor and head of Amalgam's Execution Squad, Gates (aka Mister Kallium) is completely and utterly off his rocker. In his first appearance he shoves a man out of a helicopter for questioning his predictions about how a battle may have progressed, has all his former allies slaughtered, then has a Freak Out and kills the men who did it. He later tries to ambush the heroes and kill them, using an attack in a public place as a way to draw them out. He's a truly warped sexual predator as well; he's heavily implied to be taking advantage of teenage girls Yu Fan and Yu Lan, admits to being a necrophliac, and is seen masturbating to images of kittens and squirrels. A spectacularly Bad Boss, he drowns one of his men in a pool for bringing him bad news. In the Season 2 finale, after Leonard Tesstarossa has killed one of the twins, Gates uses her corpse as part of a puppet show to taunt the surviving twin, whom he then murders, before making his final assault on Mithril.
Gauron is rather attractive for a middle-aged man.
Foe Yay: Gauron spends an awful lot of his time thinking about Sōsuke. Not to mention the whole "I love you Kashim!" thing. Or how, in the novels, he said he would've wanted to kill him and fuck his corpse.
It is now completely canon. Watch the TSR comedy radio show where Gauron acts as the school's "sensei." Gato is doing this on purpose. Gauron orders Sousuke to write on the chalk board "Kashim loves Gauron Sensei. Heart. ♥" as well as "Gauron Sensei's extreme attack makes Kashim's heart pound. I want to have children with him." Followed by what appears to be an attempt to rape Sousuke in front of the class. Yay for subtlety.
Idiot Plot: The last 5 episodes of the 1st season of the Anime rely on a hostage situation that is only possible because lots of people who know better decide it is safer to allow a proven Mad Dog killer have access to the bridge of a heavily armed warship than to try to fight him and risk him killing people.
But—but—it's Gauron, of all people! ...besides, Tessa seemed well-prepared for it, anyway (replacing the torpedoes on the submarine with duds, for instance).
They did know better; Tessa herself explictly said that the bridge crew were no match for them (having no military training). If they tried to subdue Gauron OR do nothing, he'd have killed them all and still have control of the ship, with no opposition.
Launcher of a Thousand Ships: Sōsuke. He's been paired with pretty much all the major characters, plus some side characters. Men, women, friends, enemies, characters much older than him, you name it.
He would probably believe that "shipping" would be used in its actual sense.
Les Yay (Mao has actually groped Tessa's breasts and spends an inordinate amount of time with her, often while inebriated, naked, and in a sexually charged mood.)
Also, Yu Fan and Yu Lan are first shown onscreen sharing a very intimate shower scene...
Nightmare Fuel: Gauron actually wanted to kill Sousuke when he was eleven and canonically wanted to rape his dead body. It also gets even creepier when one realizes that their countless encounters are most likely not entirely coincidence... and that Gauron is heavily implied to be stalking him, actively choosing missions / jobs that would put him in a position to see his "precious boy."
Episode 3 of Fumoffu has an interesting case when Sousuke envisions Kaname being tortured. The visual is of her being tickled with feathers, but because it's heavily pixelated, the viewer's imagination is entirely likely to fill in the details of something much, much worse.
Squick: Wait, was Gates just whacking off, and all that was shown on screen was a picture of a kitten?