One of the oddities in the Mystery Shack is called the Sassycrotch (a play on words "Sasquatch", "sassy" and "crotch") and it shows a Sasquatch wearing a pair of underwear (no genitalia visible).
Grunkle Stan makes a vulgar comment about needing to "scratch two places at once" and often makes references to scratching himself, which his niece and nephew find gross.
Grunkle Stan has suggestive magazines in his room, which we find out in the episode Scary-oke. Though briefly shown, the magazines that the viewer can see are called "Women's Swimwear" and "Fully Clothed Women." No undressed or underdressed women are shown on the covers and the scene is played for comedic purposes.
Dipper gives a merman CPR and Mabel takes a picture of them (which was a clear shot that looked like the two boys kissing) which that she jokes it's for blackmail. ("The Deep End")
A man is married to a woodpecker, claiming that it's still "totally legal".
A boy has the back of his pants partially pulled down so his friends can pour ice cubes into his pants.
One scene where Soos, who has his shirt off, is sitting in a car with Grunkle Stan. Quiet jazzy music starts to play. He reclines his seat so it is lying down, and so does Soos, and he rolls over to face Stan and says, "Sure are a lot of stars out tonight." Stan says "Welp, this is getting weird!" and immediately gets out of the car. ("The Golf War")
During the end titles in "Soos and the real girl", Grunkle Stan is in a limo with several women in bikinis.
In an episode, Dipper accidentally lays on his crush, Wendy's, bra. She mentions, "Dude, you're laying on my bra." Dipper then screams in embarrassment. Brief and mild.
The girl character is always looking for a crush, and she wreaks havoc in the shop with her "crush finder" machine
Mentions of boyfriends and girlfriends, crushes and Mabel is 100% boy crazy throughout the whole series
Romance and puberty are frequently featured themes and are the main plot points of several episodes.
One of the main protagonists has a hopeless crush on someone much older than him. This is mentioned frequently throughout the series, and is often portrayed in a vaguely suggestive way. He stays up all night thinking about her at one point, and has a vision in Weirdmageddon Part 2 of her suggesting that they can get around their age difference.
One of the main protagonists (who is 12) flirts with and has brief relationships with a variety of boys, many of whom are her her age or slightly older than her, one of whom she shares a kiss with ("The Deep End"). She hardly succeeds, however, and the scenes and flirts in are meant to be funny.
Many side characters have romantic relationships as well, but only flirting is shown in lieu of sexual content or nudity.
One character is frequently seen wearing only boxers and an undershirt throughout, in a nonsexual context. Additionally, some characters are occasionally seen shirtless, in swimsuits or in their underwear, again, in a nonsexual context.
Puberty is mentioned throughout. In several episodes, one of the main protagonists is insecure about his masculinity deals with issues such as chest hair, voice changes, sweating issues, feeling awkward, etc.
Some characters have books or magazines with sexual content; this includes characters reading "age-inappropriate" romance novels, a book about puberty ("Carpet Diem"), adult magazines ("Scary-oke"), etc. There is no explicit sexual content in any of these instances and it is presented in a comedic manner.
There are some mild sexual jokes, including one about somebody's Internet history being creepy ("Into The Bunker"), and a brief scene of somebody taking a bath with squirrels ("Gideon Rises") etc.