ACROSS from Excel Saga is probably an example (until the Gainax Ending), although that's because it would lapse into Black Comedy if they seemed genuinely villainous, as opposed to any censorship keeping them that way.
Similarly, depending on whether you think ACROSS is right or not (and given the Crapsack World that Excel Saga takes place in, it's hard to argue that they're wrong about the world being corrupt), Kabapu's group is very bad at what they do as well, especially Iwata who, ironically, is the one who takes his job the most seriously.
The Team Rocket trio from Pokémon, no doubt about it. They're actually much better at being good than they are at being bad.
In the new series, however, they've risen up to levels that make them seem more fearsome than when they first appeared, making them Not So Harmless Villains.
How I Became a Pokemon Card, a manga full of one-shots, has a protagonist named Hiroshi. He's a kid who wants to be a part of Team Rocket, but he's always accidentally doing good things. Team Rocket, in that manga, is also this, though they're depicted as being a menace for some reason.
Florsheim from Tentai Senshi Sunred has tried a few villainous schemes from time to time, but they always get caught up in helping Sunred with his love life, or saving a stray cat, or doing things that seem out of character for an evil organization. They're still fairly powerful, considering they're sentai villains, (amongst other things they curbstomp a rival organization honing in on their turf) but they aren't villainous by any stretch of the imagination.
To put it in perspective, Florsheim's "Big Bad", Vamp, favours a special brand of imported detergent for cleaning, because it's made from ecological coconut oil and is completely biodegradable. He's so harmless, he won't even resort to littering. After Armour Tiger curbstomps a rival Evil Organization who tried to take over their territory, general Vamp starts lecturing their monsters because their delinquent aesthetics are making his monsters look bad.
Emperor Pilaf and his two henchmen in Dragon Ball. He was the series' first Big Bad, but he later becomes an incompetent git who's plans are always easily foiled by Goku. Of course, he also freed King Piccolo and, much later in GT, accidentally made Goku young again at the cost of the Earth with the Black Star Dragon Balls.
Hayate Ayasaki starts his manga series like this: after having been left by his Abusive Parents with a debt he could only pay by unwillingly donating his organs, he thinks of kidnapping Nagi when he first sees her and ask for the debt value as ransom (over 150 million yen, by the way), but he does nothing but being kind to her, and never outright states his intentions...Only to turn into her savior when some thugs, well, beat him to it.
In the pilot episode of Samurai Pizza Cats, The Big Bad threatens to not invite his henchmen to his birthday party if they don't follow his orders (at least in the German dub).
He may be more malicious in the anime than in the games, but King Dedede is still pretty much as harmless in Kirby: Right Back at Ya! as he is in the game franchise. The only time he does threaten to hurt someone (other than Kirby or Whispy Woods) is when he orders the Dedede Stone to stomp Tiff - which would've resulted in her death if it weren't for her knight in shining armor, Meta Knight, coming to her rescue.
Speaking of Meta Knight, some of Dedede's Demon Beasts / monsters actually managed to hurt him - which was not what Dedede wanted.
Dr. Eggman in Sonic X. Very similarly to his AOSTH counterpart, he cooks up all kinds of ways to take over Station Square, but he fails every time. The closest he got to hurting someone (besides Sonic, of course) was attempting to have one of his robots (E-23 Missile Wrist, to be exact) crush Amy within the grip of its claws, and, similarly, attempting to have the Egg Mars crush Cosmo in its hand's grip as well.
Mon Colle Knights brings us another Terrible Trio: Prince Eccentro, Batch, and Gluko. Eccentro tries to be as evil as his father and Chuzaemon trained him to be, but he doesn't seem to go anywhere near even putting the slightest hurt on someone, and as a result, he and Batch often get punished by Chuzaemon with back-breaking exercises related to each episode's content. Gluko rarely gets punished, however, considering how airheaded and cheerful she is all the time even when she, Prince Eccentro, and Batch are always losing to the heroes.
Does anyone remember Clawdia from Fighting Foodons? She's another classic example, being incapable of even stealing a certain item such as Chef Crock Pop's scroll (which she ended up replacing with an empty fake scroll) or even the ultimate recipe held at Hamsterdam (in fact, what she got instead, to her embarrassment, was a pair of underpants), and can't even come anywhere near beating Chase and/or any of the other good chefs. One of the times she actually came close to winning for once was siccing a seemingly-indestructible Bearafooda on the good guys in Episode 10 (who of course gained back the upper hand when they used a power topping). She finally got one more chance to impress King Gorge in the third-to-last episode and she blew it, of course (which in turn leads to Gorge to attempt to kill her as punishment only for Chase to stop him, after which she later redeems when Chase and the others break Gorge's spell on her with their food).
In Kyo Kara Maoh, Stoffel is an interesting example, in that he was an Evil Chancellor in the past, manipulating the previous Maoh (his sister!) to some pretty extreme ends and generally causing a lot of damage and sorrow to a lot of people. But his villainy is all about politics and manipulation: in the current timeline, the new Maoh's advisors keep a close eye on him, and Yuuri himself is Too Dumb to Fool into being politically manipulated, so after spending his first appearance trying and failing to win Yuuri's favor and nearly starting a civil war, Stoffel becomes a comically inept sycophantic toady in short order.