To what degree are we talking about when you say "fucking up the world?" That would have been my suggestion, tbh, but I wanna be sure that we'd be discussing the same thing.
Like, the way I see it, while every failure should be an opportunity, those opportunities don't necessarily have to allow you to still achieve your original goal, or do so in the same way. For example, let's say that if the PCs fail at a thing, the world is fucked. They fail, but the failure should be an opportunity, but that doesn't me they should be able to find a way to prevent the fucking of the world; rather, the world still gets fucked, but because of the circumstances of the failure they have a chance to unfuck it.
That arc of Teen Titans with Trigon would be a good example: the Titans fail to ward off Slade and Trigon's minions, and also fail to convince Raven not to go through with becoming the portal, but as a result of Raven knocking them out they aren't turned to stone by Trigon, giving them the chance to save the world.
Or say your assault on the Fire Nation's capital during the solar eclipse fails (possibly because of an earlier failure that left you alive, but unable to use the Avatar State), and thus the war continues and many of your NPC allies are captured, but you are able to escape and ultimately gain Zuko as a companion.
tl;dr failures should be opportunities, but they don't have to be opportunities that allow the PC to proceed linearly, also Teen Titans and Avatar are good television.