It's a me! Mario-o...oh...oh, my.Super Mario RPG: Legend of the Seven Stars
This game has a variant of the classic Mario villains, "Shy Guys." These versions are known as "Shysters." It's also a word describing an unscrupulous person (particularly lawyers) that has tended to carry an anti-Semitic connotation.
Yaridovich claims, "I got to my lofty station in life by... ahem... 'pleasing' my superiors."
Valentina's 'hit' animation seems to involve little but gainaxing.
If you look around her bedroom, you can find Princess Toadstool's "???". We're not told what it is, but her grandmother will immediately run over and bribe you to leave it be. Go back and find it again when the princess is in your party, and she will yell at you for going through her things. The original Japanese name is "Peach's XXX", but in Japan, "XXX" is typically used in the "insert word here" sense, making it have the same meaning as ???.
Many fanartists have jumped on this odd lack of description, usually interpreting it as being underwear of some sort. Except when they decide it's something else a lady might keep hidden in her bedroom.
One of King Calimari's (a gigantic octopus, for the record) attacks is to use one of its tentacles to snatch away one of your party members. When they're returned to the battle a few turns later, they'll have gained the "Fear" status. Hmm...
Paper Mario
One quest involves returning a "special tape" from Goompa in Goomba Village to Koopa Koot in Koopa Village. The contents of the tape are never mentioned, save that Goompa keeps it... well hidden.
During the scene where Peach can disguise herself as one of Bowser's troops, you can interact with a particularly flustered Hammer Bro in the library. He protests that he's not looking for "that book", and bribes you to leave.
Paper Mario: The Thousand-Year Door
Similar to the tape from the first Paper Mario, this time with a mysterious 'package', from one Goomba to another. Add to this the fact that this delivery is made in the back streets of Rogueport, and the Goomba for whom you're delivering it tells you not to be seen, well, it just speaks for itself really. This happens in the third game as well.
A very easily missed "crap past the radar moment" is when Mario is trapped in the cage by Crump in Chapter 2 with all the Punis. Use Goombella on Puniper [the big Pun]) and she'll say, "That's Puniper of the Punies. He's a little bigger than the others, obviously. So maybe he can help us reach that special area... Hee hee! Just kidding. His only special power is complaining, I think." 'Special area' would not be that suspect if she hadn't immediately gone, "Just kidding." This tattle, by the way, only occurs when you are in the cage — after you get out of the cage and free the Punis, you'll get a different tattle.
Also radar-dodging is one of Kammy Koopa's lines after her visit to the Glitz Pit, regarding shaking what her momma gave her — in wavy text to emphasise it.
The between chapter Peach segments contain a few instances of Fanservice that managed to scoot by the radar. Some chapters allow you to have Peach take a shower before meeting with TEC (the first chapter requires it) and one chapter has Peach pull an Invisible Streaker to sneak around the enemy base. Nothing is shown on screen, mind you, but even the implication of nudity is surprising for a Mario game.
Super Mario Sunshine
When Bowser Jr. claims Peach to be his mother, Peach has to think about it first before saying she isn't.
She actually never claims to not be his mom! (Bowser tells his son the truth in the ending cutscene.) Peach is likely hesitant to correct Bowser Jr. because of the bizarre nature of the situation, but still.
Busy day, you know? Get carried around by some Mario imposter by the waist, roast around in the heat, get taken to some park and stuck in a high place... I'd be having a hard time registering things (truthful or not) too. I'd also be very dizzy, probably.
Koopa: Now is hardly the time or place for that, Lena.
Getting "Love is a Drug" on the Boom Boom Bar's jukebox.
Super Mario World (series)
Luigi scolds Yoshi after eating the cave peoples' rescued crops.
Luigi: Well, since you ate the whole thing, now you can do the hoe thing!
Super Mario Galaxy/Super Mario Galaxy 2
In both Super Mario Galaxy and Super Mario Galaxy 2, the Queen Bee actually wants you to crawl all over her body (to collect five Star Chips that are making her itch).
Listen VERY CAREFULLY to the song Fishing Frenzy, at 40 seconds in. You hear a snippet from the song "think ya better D". Specifically, you hear the lyrics, "bitch, what the fuck do you got to lose". Two verystrong swear words, in quick succession, in a Mario game! You know the ESRB radar missed this because Mario Mix doesn't have a "Lyrics" warning on the cover.