Mr. Simmons and his sexuality. It's not hidden, even though he's very obviously gay, yet not stereotypically so or even mentioned. Word of God has confirmed this and the character's voice actor, Dan Butler, is himself openly gay.
The Thanksgiving episode even gives us what is very obviously his boyfriend/life partner butting heads with his mother (who spends most of her time not-so-subtly urging Mr. Simmons to date a female friend).
Pearl: I didn't know Peter was coming.
Peter: There's a lot of things you don't know.
In the Beach Episode, both Mrs. Kokoshka and Miriam are invited by a typical Romantic False Lead to a stimulating dancing class. After hearing the "stimulating" part, they both giggle. And for the final blow, the class is only shown off screen, with the women saying "Ooh, you are so wonderful dancing!"
When Miriam told Bob about learning "the Watoosie" from a man named Carlos, he was obviously uncomfortable with it. Then again, since he was sun-burnt all over his body, he might have wanted someone to take care of him.
In the episode "New Teacher" when Mr. Simmons is trying to teach the class about poetry, Harold stands up and recites, "There once was a man from Nantucket..." Mr. Simmons tells him to sit down before he can get to the next line.
Which is, as everyone knows, "Who kept all his cash in a bucket." Interrupting it allows you to infer he was going to recite the other version instead, making it naughtier than it actually is.
Pretty much every episode featuring Wittenburg and Tish ends with the implication that they're about to have make-up sex.
After Helga's confession in The Movie, and an awkward kiss, Arnold states he's dizzy, and needs to go lie down. Helga's response: "Wonderful...I'll go with you!"
In the episode where Grandpa thinks he's dying, he wakes up and believes that he's in heaven. When he sees Oskar however, he panics and says "This must be that other place!"
In the Latin-Spanish version he actually says "I must be in Hell!"
Also alluded to in "Haunted Train" when Grandpa is tilling the titular urban legend, using "fiery underworld" in place of hell. In that same episode, Gerald sings a song about the train with a verse describing how the engineer "drove it straight to..." but he finishes with "Hey!" instead of hell.
We get this little gem from "Back to School":
Arnold: You're not too old, Grandpa, and you've still got plenty of brain cells. Grandpa: No, not since Woodstock.
Curly's Stalker with a Crush interest in Rhonda is anything but subtle. He's constantly suggestively telling her to "Give Daddy some sugar..."
"Grandpa's Packard" features this exchange.
Ivana DeVansovich: Wonderful. I simply love your car. It's so well-preserved.
Grandpa: That's not the only thing well-preserved around here, lady. *eyebrows move up and down*
In "Buses, Bikes, and Subways," Arnold's class sings an uncensored "99 Bottles of Beer on the Wall" in unison on the bus with Mr. Simmons happily conducting. Not very shocking, but compare to other cartoons, which would replace "beer" with something else.
Helga mentions that she performs "Tantric spells" towards the end of "Helga On The Couch". It's a pretty clever one too. For those who don't know, Tantra is a subset of Hindu spiritualism revolving around the carnal (read: sexual) aspects of human physiology, and it has rituals (often misidentified as "spells") nominally used for inducing lust in a person (it's where the expression "tantric sex" comes from). In short, Helga is using Hindu spiritualism to seduce Arnold.
During the episode "Summer Love," Grandma stumbles across a private nude beach, which she then says "When in Rome..." and takes off her bathing suit. All the beach goers run away screaming. On top of that, the nude beach is called, "Mature Wood Private Beach"
Actually, since he is presumably referring to a donkey in the above scene, that wouldn't actually be swearing. A donkey is an ass. However, some American TV shows (particularly kids' shows) will censor a curse word that has (or had) a legitimate meaning (like "dam" if it's used as a pun for "damn" or "hell" if it refers to the actual pit of despair for those who were evil in life).
Similarly, in the episode "On the Lam," Harold, Stinky, and Sid pull a school prank with a bottle of Jack Ass Kicking Louisiana Hot Sauce.
In another episode, Helga recited some of her obsessive love poems in the presence of a parrot, who then flew off and almost repeated it to Arnold. The poem was standard fare for Helga; obsessing over Arnold, flowery language, and such. One line, however, was "you make my girlhood tremble, my senses all go wacky." Whether it's innocent or dirty really depends on who's listening, though seeing as she composed it in her sleep, it can be interpreted as an erotic dream.
In the same episode, she ended up watching Arnold undress and then passed out with a very happy face.
Similarly, in "Helga Sleepwalks," it's established that Helga's sleepwalking spells are tied to her subconscious desire to tell Arnold her secret. With that in mind, one of her sleepwalking spells has her end up showering in Arnold's shower, forcing one to wonder where her subconscious was going with that.
In "Ghost Bride," Arnold reads this tombstone aloud with the rest covered in grass: "'Here lies Cynthia Snell. She lived her life and went straight to'...I can't read the rest."
In the very same episode, it shows the backstory of "The Ghost Bride" as graphically as the censorship would allow them which included her brandishing an ax towards the couple's home, the shadow of the ax coming down on them with psycho strings playing, she sitting next to the murdered corpses humming the wedding march and then jumping out the window.
There was also a late-run episode in which Arnold found his father's journal which his Grandpa Phil begins to read aloud to the family. When he gets to his father's account of his wedding night Phil starts to read the words "It was the hottest night the jungle had" and the flashback showing us Arnold's parents in a hut seductively looking at each other... as Phil uncomfortably trails off from reading and distracts Arnold with thoughts of ordering dinner. As soon as Arnold leaves the room Phil rips out the page and hides it.
Speaking of Grandpa's war stories: There was that (made-up) flashback in the "Veterans Day" episode with Adolf Hitler in it. His name is even said a few times.
Arnold: You did not fight Adolf Hitler, you're making this all up.
Grandpa: *laughs* Okay you got me, I made that part up. Pretty funny huh *laughs* It was Goebbels.
Part of Grandpa's story involves him staying the night at a farmhouse, with three beautiful french women. The oldest one, Monique, visits him in the night in a figure flattering diaphanous dress, to tell Phil that the war has made her feel scared and lonely...Gerald's father then urges him to skip over this part of the story, since it was clearly headed in an erotic direction. Looking at Arnold and Gerald's reactions to the interjection, it seems like they wanted to hear it. When Phil resumes the story, he recalls that he woke up the next morning "feeling like a million bucks."
In the episode "Helga's Love Potion," Helga says "What is this crap?" while reading one of her poems after the spell to get rid of her obsession with Arnold gets cast on her.
Helga, Harold, Mr. Potts, Dino Spumoni, and others said "crap" and variations of the word so many times that it is unlikely that the word was on the radar at all. Helga also says "freakin'" in the episode "Helga's Locket" and Torvald says "sucks" in "Tutoring Torvald."
Miriam's alcoholism. Even Word of God says that she's an alcoholic, but the Nickelodeon censors told Craig Bartlett and the writers they couldn't outright say it, so what do they do? Have her as a depressed, narcoleptic smoothie addict (never mind that some alcoholic drinks do exist as smoothies — piņa coladas, hurricanes, daiquiris, etc). Also if you pay close enough attention when she is grabbing ingredients for a smoothie she grabs Tabasco sauce. There are even hints that she was busted for at least one DUI. One episode has the kids shocked that she apparently got her driver's license back and another has Bob casually remark that she's supposed to start community service that morning.
In the Swedish dub, Helga has gotten away with saying "What the hell" and "Damn".
"Fishing Trip" starts with the guys singing "Miss Susie" in the car and in the end Davy Jones sings the whole song.