The Absolute Worst Thing Goku Has Ever Done
Though the English dub of Dragon Ball Z did its best to make Goku more of a Superman figure, as opposed to his harsher depiction in the manga, it couldn't hide the fact that the Saiyan isn't always so pure of heart. Outside of combat, where power levels are no longer the name of the game, Goku is a pretty carefree guy — but that doesn't excuse some of his boundary-stepping antics.
Many of Goku's more questionable actions can be chalked up to his approach to battle: he always wants to fight opponents at their strongest. That mindset isn't what any sane person would call a healthy one, particularly not when it results in maniacs like Frieza and Cell being allowed to wreak even more havoc, at the expense of an exciting duel. Yet, for all that, Goku's worst indiscretion is only indirectly tied to fighting. Instead, it directly involves what is quite possibly Goku's largest blind spot: Women.
Goku's history with women
Having essentially been raised in the wild by his grandfather, Goku didn't receive much in the way of an education. He's beyond brilliant when it comes to duking it out, but he's lacking in a wealth of other areas, one of the most egregious gaps being his human interaction skills. He cares deeply for his friends, but the day-to-day handling of those relationships can be ... rocky. This is doubly true for the women in his life, especially in his early days. His grandfather taught him to be respectful around the opposite sex, but theory and practice are two different things.
Upon meeting Bulma for the first time, a young Goku lifts her skirt to check if she has a tail like him. His first encounter with his wife-to-be, Chi-Chi, doesn't go much smoother. To compound the problem further, witnessing Yamcha's lady-related failures, as well as Master Roshi's womanizing, doesn't improve Goku's understanding of women as he grows up. Thankfully, he doesn't become a womanizer himself, but he's as aloof as ever: When Chi-Chi sees him again for the first time in years — both of them now in their late teens and pitted against one another in a tournament — Goku fails to reciprocate her affection, not because he has no feelings for her in the traditional sense, but because he has no idea who she is. Whoops? Jogging his memory is an admirable feat on Chi-Chi's part, to say nothing of never divorcing the Saiyan, later on.
Regardless, it's safe to say Goku spent much of his early life so focused on training that he never figured out these basic life skills ... which leads to what is, arguably, his most disgusting offense.
Goku's deal with Old Kai
In the episode "True Saiyans Fight Alone," the insanely powerful Kid Buu has destroyed Earth, and the heroes are looking for a way to restore the planet. So they visit the Sacred World of the Kai, god-like beings who could potentially grant Goku's son, Gohan, enough strength to finish the fight. Of course, simply asking for such power isn't going to cut it, so Goku decides to strike a deal. Now, if there's one thing Goku knows about his old master Roshi, it's that he's a lecherous cretin. The elder Kai, known as Old Kai, seems similar enough to Roshi, so Goku uses that as leverage, promising the god a chance to fondle an Earth woman. The proposition is messed up enough on its own, but then Goku suggests Videl ... Gohan's girlfriend.
First off, this is a father offering his son's girlfriend to another man. In any other context, this could easily lead to jail time. Second, Videl is a minor, making the whole thing even creepier. Gohan, obviously, refuses. Goku's next ploy is to offer Bulma. Old Kai accepts, and when discussing using the Dragon Balls to restore earth, Goku assuages the god by reminding him that Bulma's waiting for him — saying this in front of Vegeta, her husband. Vegeta has every right to be angered at the comment, but he's not innocent either, since he suggests for Goku to offer Chi-Chi instead.
His response? That Chi-Chi's not as pretty as Bulma. Yeah. Problematic and sexist stuff, all around. Universal threats are par for course in the Dragon Ball franchise, making a lot of Goku's combat-related actions less shocking than thrilling, but this series was never the most progressive when it came to handling its female characters.