There's a long-standing theory that without superheroes there wouldn't be any super villains. They rise up in response to the theatrical good guys. Refuted as namby-pamby BS that will get Gotham killed by The Joker in Miller's Dark Knight Returns, it still has some resonance.
Even in Dark Knight Returns, honestly, Batman solving some of Gotham's problems doesn't mean he didn't help cause them. Even if superheroes aren't the cause of and solution to all of life's problems, there are numerous occasions where they've come into a bad situation and made it horrible. And not just as the plot of most episodes of Teen Titans Go!
10 The New Warriors Vs Nitro
A massive supervillain escape from Ryker's Island is pretty bad, but it's nothing that explosions can't make worse.
In 2006, Speedball's team the New Warriors were portrayed as inexperienced glory seekers. When they tracked down a group of escaped bad guys, they did what superheroes do and attacked without calling in backup. This was fairly standard hero procedure, except Namorita captured Nitro by using a school bus as a backstop. This was bad form on her part, and not realizing that Nitro's power was self-detonation was worse. Most of the heroes and villains were killed in the explosion, along with the kids on the bus, and around 600 other people. Even worse than the happy-go-lucky Speedball donning a spiky gimp costume as the self-torturing Penance was the resulting...
9 Civil War (Like, All Of It)
A world full to the brim with untrained super people isn't an ideal situation. Forcing everyone with super dishwashing powers to register as a deadly weapon was also a transparently bad solution. Tony Stark and his contingent of good guys campaigned for this concept aggressively. When some heroes predictably resisted outing their secret identities and endangering their loved ones things spiraled out of control.
Any "solution" that results in villains hunting heroes in U.S. government-sanctioned hit squads, the Green Goblin running The Avengers for years, and Captain America's assassination is a bad solution! Way to respond to a single horrifying incident by creating a massive, liberty-destroying horror Tony.
8 World War Hulk
The Hulk's existence is a bad situation. He's basically an apocalyptically powerful baby raised in a world without love. Even though he's saved the world more times than Buffy, any time he enters city limits he's probably knocking down an office building. Still, mental healthcare was a better solution than sending their buddy into deep space. Especially since the Marvel universe is a densely populated place!
When a furious Hulk returned to conquer Earth with an army of alien gladiators, why was that a surprise? Given the number of cosmic empires Marvel's Earth has encountered it should have been more of a shrug and not a Whole World Caught With Pants Down shock.
Super genius Hank Pym had some problems. He was super smart, super jerktastic, and super lonely. His solution was to make like Geppetto and build a Real Boy. Why he equipped his new robot son with a mind-erasing weapon we'll never know, but it was a critical blunder. Even though Ultron's electronic mind was based on Hank's brainwaves somehow he'd created a major nemesis.
Ultron wasn't just a nemesis for Hank, or the Avengers, but for human life. Constantly constructing new bodies from (apparently plentiful) adamantium, the number of possible futures where Ultron has wiped out human life are incalculable. Not a good solution to a personal problem, Ant Dude.
6 Captain America 'Saves' The Winter Soldier
The death of Bucky Barnes is a complicated tragedy. He was not only apparently killed by Nazis but captured and mindwiped by invading Soviet forces. As the Winter Soldier he was frozen and only thawed out to murder inconvenient people. Decades were passed this way until Cap was able to rescue Bucky and restore his memories with the Cosmic Cube's science genie.
Suddenly, Bucky knew what he'd done and it broke his heart. Breaking the mind control was a good idea, but a more specific wish could have spared Bucky a lot of PTSD and suicidal ideation. Cap found the worst possible way to rescue his old friend.
5 Kingdom Come's Gulag
The DC Universe has its own catalog of disproportionate sins. The beautifully painted Elseworlds story Kingdom Come envisions an America overwhelmed by undisciplined super gangs and ineffectual heroes. Captain Atom's death even destroyed Kansas, proving things are dire. The old school heroes rally, though, and build a Gulag for super baddies in irradiated Kansas. The place is evidently understaffed and stuffed to the brim, though, and when a massive breakout leads to a NUCLEAR STRIKE that kills almost all of the heroes and villains on Earth!
We have achieved Worst Situation, y'all. You'd have to, like, blow up a planet to make things worse.
4 John Stewart Blows Up Planet Xanshi
In 1988 Green Lanterns still had a fatal weakness to the color yellow. The Corps' fatal flaw was apparently a well-kept secret, so when ex-Marine John Stewart showed up on Xanshi wielding the universe's most powerful weapon he figured he could handle anything. He was hunting a universe-eating bugaboo alongside J'onn J'onnzz and John thought one of the League's strongest members would slow him down.
He bubbled J'onn and went to face the Badness on his own. Amazingly, Badness was yellow, and he was powerless to stop it from destroying not just Xanshi but Xanshi's entire solar system. If John hadn't banished his partner just for LOLs then the Martian probably would have handled the situation.
3 Superman Clashes With Captain Marvel
Back in the days of Justice League Unlimited, when Shazam! was named Captain Marvel, the good Captain joined the Justice League. Secretly being a kid, though, he accidentally endorsed Lex Luthor's presidency. Making things worse, he also showed up at an unveiling ceremony where Luthor was introducing a high-tech, low-income development he was funding. An irate Superman showed up too. Marvel tried to defuse the situation but instead started a fight with the Man of Steel. Between the two of them they obliterated Lexor City and left a lot of kids homeless.
Neither hero comes out looking great. Superman usually absorbs most of the blame as the more experienced hero, but Marvel never made anything better even once in this episode. Super heroes and their super mistakes.
2 Nighthawk Tries To Save The World
In 1985 the idea of a benevolent superhero team conquering the globe was novel. The Squadron Supreme, Marvel's near-parody of the Justice League, suddenly got very serious as a result. Led by Hyperion, a sympathetic faction of heroes overthrows the world's governments, bent on finally making a real difference. This sparks a Civil War with Nighthawk's faction, and we end up with a very lethal argument between faux-Superman's and faux-Batman's teams.
It's hard to say which side was better at making things worse. Hyperion got good results in the short term, but set up the planet for a potential eternal dictatorship. He was replaced by an evil version of himself for a while, making this scenario even more immediately plausible. Nighthawk, though, picked a murderous fight when what he probably needed to do was establish a dialog with the frustrated heroes. Worse, he had no plan for what to do if he won. His best case scenario was global chaos. His actual result was a lot of murder, including his own.
1 Captain Amazing And Casanova Frankenstein
In the 1999 film Mystery Men, Captain Amazing is Champion City's superheroic defender. He's also a sell-out. Worried when he starts losing endorsements, he frees Casanova Frankenstein just so he'll have a decent villain to punch. Then he loses said fight, leaving Champion City defended by the C-list heroes, the Mystery Men. Based on Bob Burden's Flaming Carrot comics, the team of semi-competent heroes are fun but semi-effectual. Good, bad, or indifferent they manage to sneak into Casa de Frankenstein and almost rescue Captain Amazing. They flip one too many switches, though, and literally melt Amazing's face. Counts as making things worse, everyone.