A surprising instance from the 4Kids dub was when Captain Morgan had "Zolo" before the firing squad and proclaimed that they were going to "riddle him with more holes than a fishing net."
Another violence-related example occurs during the Baratie arc, where a visual representation of the explanation of "Red Foot" Zeff's nickname leaves the blood coating Zeff's foot completely intact. While the dialogue doesn't refer to blood at all, the words chosen make it clear that what we're seeing is neither paint nor any sort of fruit juice.
Captain Buggy, one of the earliest villains the Straw Hat Crew fought together, has a type of cannonball that he named after himself, called the Buggy Balls. The awkwardness of this name is taken Up to Eleven with phrases like "Prepare my Special Buggy Balls!"
Another surprising instance in the 4Kids dub is when "Zolo" said, during his fight with Mr. 1, "Is he made of steel or steroids?". To think, they edited so many drug references... However, by then, the show was airing on Toonami, so....
One instance that should really be noted is that Kalifa's Awa Awa no Mi means that she's a Soap Girl. In Japan, Soapland is a term for certain kinds of brothels where, officially, the client is only "bathed".
The second movie has two members of the Big Bad's Quirky Miniboss Squad kidnap Nami, so she can be forcibly married to said Big Bad. However, the kicker comes when one of the members announces that they'll have lots of fun seeing him do this and that to Nami. As the crew repeats "this and that" with disturbed-looking faces, what follows is an Awkward Pause...and then the other member blows up their boat.
There are a lot of really dirty jokes and allusions in One Piece. Zoro telling Nami he's wearing bandages because he lost his shirt (in the English dub only) and doesn't want to distract her. Nami telling Dr. Kureha, who was telling Nami not to tempt Chopper to their crew, that she doesn't need the Doctor's permission to hit on guys. Dr. Kureha calling herself a swinging single.
There's the 2nd TV special where a young girl named Amanda is kidnapped and Mind Rape'd to slowly undress, only to reveal a map on her back. Of course, by the length of the scene and the look on poor Amanda's face, it's obvious she feels violated.
That's nothing, the Italian dub (which has 4Kids-like levels of censorship) aired the whole scene unedited!!!! You may now kneel in shock and awe. To be honest however, they don't specify what Robin's holding and instead says "It's Hurting him!".
When the Amazon Lily warriors try to pull out that one "mushroom" from inside Luffy's shorts. For all intents and purposes, Luffy's getting a handjob - granted that, of course, he's unconscious at the time. They also wanted to take off his jewels.
In the anime, we hear it "stretching", just to drive the point home what the mushroom actually is.
Fake Robin trying to bait Chopper with a cucumber. She has... quite the way to offer it. Thank God Chopper didn't bite it. In more ways than one.
Nami asks Chopper if he wants to try out the Shower Tempo...while she's in the shower herself.
Nami's Shower Scene during the "Friends' Wherabouts" episodes in the anime briefly displayed her entire butt onscreen. How they got away with this is pretty obvious though - her butt is so low detail and simplistically drawn it can barely be called a butt. (Compare to Nami's far more detailed body proportions in other sequences, such as the Shower Scene in Thriller Bark)
During the Skypiea arc Usopp uses a self-propelled grappling hook called the Usopp AaUwaUwa. If the fact that it's launched from the center of his belt isn't enough to put your mind in the gutter, his exhibitionist-like pose when firing it should do the trick.
Near the end of the Skypiea arc, Luffy has a giant ball of gold attached to his arm as a "gift" from the Big Bad to keep him out of the way. As Luffy struggles to try and force the gold off his arm, he says "It's hard to get this golden ball off!" The response from Aisa? "Watch your mouth!!"
Counts as a Double Entendre in the Japanese version, as the specific word Luffy uses for 'golden ball' can actually mean testicles.
Sanjida (who's supposedly a female Sanji in the Obahan Time special, though she's still voiced by Sanji's voice actor) likes to touch other females.
Obahan Time also features Namijima, the middle aged woman of once-a-month justice. She tells off the middle aged pirate gang once a month for some reason. Turns out she rampages to claim rent money.
This wasn't probably intentional, but when Monet's suicide bombing is animated, there's a lengthy scene where she prepares mentally to die. It is supposed to be an emotional scene, but her loud breathing caused surprisingly many people have their minds in the gutter.