This ends up being deconstructed in Avengers (2016)'s .1 story, set during the "Cap's Kooky Quartet" era. The public isn't keen on Captain America leading a team of former super villains, Captain America himself isn't keen on leading a team of super villains (especially since Iron Man, Giant Man and the Wasp dumped them on his lap and said "We're quitting!"), the former super villains aren't keen on being with each other and, when they're thrashed by the Frightful Four, the Wasp is horrified and realized they made a terrible mistake.
British war-oriented comic Battle Action included a British Empire Dirty Dozen clone called The Rat Pack complete with cockney thug/knifeman/marksman, sneaky little pickpocket and gigantic musclebound Turk. For some reason these "Convict Commandos" wore blue battledress rather than Khaki or green.
Mercilessly parodied in The Rifle Brigade where fearless Captain "Khyber" Darcy leads Ambiguously Gay Lieutenant "Doubtful" Milk, monstrous Yorkshireman Sergeant Crumb ("'ey oop"), Cockney thug Corporal Geezer ("Yer aht of ordah!"), Private Hank the Yank ("Gawd Dammit!") and The Piper (who isn't an actual soldier but is still probably the most brutal of the lot) on missions against.... well you really just have to read these for yourself! But to give you an idea on the type of operations entrusted to the Rifle Brigade, one of their most important assignments involved recovering a powerful arcane artifact before the Axis could get their hands on it. The artifact was Hitler's missing testicle.
Captain Darcy would eventually lampshade the squad's existence by saying that there's always been a place for a Rifle Brigade in the British forces, and that there was a Rifle Brigade-type collection of misfits before there were rifles, because "when you get down to it there's some things ordinary chaps just can't do!"
The Rifle Brigade was also likely a parody of Sergeant Fury's Howling Commandos, the Leatherneck Riders, and the Deadly Dozen. Notably, Doubtful takes the place of Percival Pinkerton, while Hank the Yank is the token foreigner (again, Pinkerton), Crumb the gigantic Bruiser (Dum Dum Dugan), etc.
Basically, pick a war comic. Even the stark realism of Sgt. Rock's Easy Company leans this way, featuring the mild-mannered Wildman (whose name comes from his secretly having a Hair-Trigger Temper), one armed bazooka expert Zack, nebbish bespectacled sniper Four-Eyes, clinically anxious Worrywart, etc.
The Suicide Squad in The DCU. A covert program of the U.S. government that keeps sending villains (and a few heroes) on suicide missions until they've earned release from prison... or they die. Think The Dirty Dozen with superpowers (some of them, anyway). While literally every incarnation fits, the Injustice League version is the most apt, with Major Disaster, Big Sir, Clock King, Cluemaster, and Multi-Man. The subversion happens when all of them die in the first issue except for Major Disaster.
The original Suicide Squad was a WWII unit simply composed of notable or exceptional soldiers. However, apparently the top brass and the recruiting officers didn't collaborate very closely on this one, because the resultant team was composed entirely of antisocial hotheads who hate each other more than they do the enemy, hence the name.
Subverted in Kyle Baker's Iraq war satire Special Forces, where an army recruiter desperate to make quota so he doesn't get sent back to Iraq recruits a ragtag bunch of misfits, falsifying records to recruit criminals, drug addicts, those mentally or physically unfit for service, and others who by all rights shouldn't be in the army, but ends up having to serve alongside them when one of them goes off his meds and gets himself killed before boot camp. By the end of the first issue, he and all but two of his recruits have been slaughtered.
For the record, the surviving members are Zone, a severely autistic young man who doesn't talk and follows orders with machine precision, and Felony, a nineteen year old girl with an extremely colorful criminal record. Yes, they were both in a front line infantry unit.
Also from The DCU, Gail Simone's Secret Six, a team of mercenaries who are spectacularly messed up, and know it. Their enemies are even worse.
Yet another DCU one, The Losers, several military men who for one reason or another are off official duty and now serve covertly; they're called the Losers because they have nothing left to lose (try understanding the idea behind that), and include Captain Storm, a one-eyed, one-legged salty sea dog if'n thar ever were one, and Johnny Cloud, who was genuinely heroic and uber-competent but insisted on being a Loser because, well, he felt like a loser. He usually flew alone, but one day took a brash new pilot with him. They were attacked and forced to crash. The new pilot lost his life; Cloud joined the Losers after that.
The original ABC Warriors; Hammerstein is a warhorse famous for his strength and leadership skills but rumored to have murdered a human superior, Joe Pineapples is an ace marksman who once killed a target from orbit but is perhaps the most unsavory being in the universe, Happy Shrapnel is simply dumped onto them because as an older model he's not very user friendly, Mongrol is a monster of metal who is constantly full of only rage and confusion, Mek-Quake is stupid, violent, and crude, Deadlock is an extreme Knight Templar, Blackblood is known for murder at the slightest provocation, Steelhorn is the original veteran of the Volgan War turned into a horrific mess of molten slag, and so on and so forth. They're the most capable combat unit fighting the Volgs, but goddamn.
Later additions only enhance this image; Mad Ronn the bomb disposal expert (whose skill at his profession is uncertain because he kind of dies the first and only time he actually tries to defuse a bomb), Hitaki the warrior with samurai programming, Morrigun the waitress whose combat skills come from secondary bouncer software, and Ro-Jaws, who is honestly more of a mascot than anything else. Morrigun was the result of a Terrible Interviewees Montage; you should see the guys they turned down.
They get a lot of flack for this, and their most major enemy makes fun of them for it, noting that they don't really have any A-list level people on-board. It also makes trying to get people to listen to them when they say there's trouble all but outright impossible.
The Defenders, comprised of heroes who don't work well with others, and who often get into fights in the middle of their missions, still manage to be successful because they are comprised of some of the most powerful heroes in the Marvel Universe. They're even famously known as a "non-team", because the concept of teamwork is completely alien to them. This is all in spite of the fact that the founding Defenders (Doctor Strange, the Silver Surfer, the Hulk, and Namor the Sub-Mariner) are among the most powerful Marvel heroes of all.
The second team of X-Men, especially in comparison to the original team. The first group were five white, American teenagers, recruited by Professor X as students for his school, given matching uniforms, and trained to work as a group before their first mission. The second teamnote even going just by what was known at the time, and ignoring things that wouldn't be revealed or even RetConned in until later, like Wolverine being Really 700 Years Old or Storm having been born in America each came from a different country, including no members who were both white and American (and one that was blue); varied from their teens to middle age; came from backgrounds ranging from law-enforcement to former supervillain (including one that was both); ranged in education level from college graduate to "raised on the streets"; were all given unique uniforms (or just wore what they showed up in); and barely had time to learn each others' names before being sent off to risk their lives.
The Great Lakes Avengers is a team comprised of some of the weirdest superheroes in Marvel's catalog, including Flatman, Big Bertha, and most popularly, Squirrel Girl (whose superpower is . . . squirrels). It doesn't hurt that Deadpool is considered one of their reserve members.
In both B.P.R.D. 1946 and 1947, the Bureau of Paranormal Research and Defense finds itself working with one of these. In the first, it's a squadron of problem soldiers who've been together since D-Day — and have been causing trouble since the end of the war out of frustration for not being allowed to go home. In the second, it's shell-shocked paratrooper Jacob Stegner; Simon Anders, a merchant marine who survived 24 days lost at sea in a lifeboat; Gabriel Ruiz, a Latino jungle warfare specialist who tried to sue the USMC for discrimination; and Frank Russel, a bomb and mine disposal expert who served with distinction in Africa - and chose the BPRD when offered an officer position in an intelligence org of his choice. The first group was assigned to aid Professor Bruttenholm during his time in Berlin - because all the army had to spare was soldiers. The second was a collection of agents available for immediate deployment.
The New Avengers are a team more or less thrown together by circumstance (they were on the "losing" side of Civil War). Even now that they can work openly, they remain a group without a great deal in common except that the team is a sort of refuge where they can get themselves back together and get on with their lives.
You don't get much more "ragtag" or "misfit" than Doom Patrol. They're the superheroes that even other superheroes consider too weird. When Beast Boy is considered one of the most mentally healthy and scary-competent members of the team, you know it's bad. Turned out to be an Invoked Trope by their Magnificent Bastard of their financial backer/leadership/Mission Control Niles "The Chief" Calder.
Astérix, Obelix, Hemispheric, Selectivemploymentax, Gastronomix, Neveratalos and Ptenisnet in Asterix the Legionary.
Red Hood and the Outlaws: So far, 3 former Titans, 2 of whom are failed ex-sidekicks. The resurrected, violent, mildly crazy Red Hood, who managed to get kicked out of the Batfamily after coming back from the dead, is The Leader. Former alcoholic and Arrow family dropout Arsenal (even with the most traumatic bits retconned out) and Princess Koriand'r... who as a young child was sold into slavery by her sister, to save her home world, spent much of her life in death camps, and doesn't really remember a lot of things concerning Earth clearly. Which is good, because Red Hood tried to kill someone she deeply cares for. Several times. And nearly killed their mutual brother, whom she was a teammate of.
In Transformers: More than Meets the Eye, the Scavengers are a group consisting of the worst Decepticons alive, according to the Decepticon Justice Division. That said, they have just enough savant-like talent, pragmatism, and dumb luck to survive. The Scavengers also reveal Hidden Depths when they prove willing to fight the Decepticon Justice Division on their newest member Fulcrum's behalf. They even get away from that encounter with only one casualty, which is a lot better than the fate of everyone else who ever faced the Decepticon Justice Division. Fulcrum declares to Tarn that the Scavengers made him proud to be a Decepticon again and that each of them is worth ten of the Decepticon Justice Division, whom he considers to be nothing more than a bunch of sadistic psychopaths who used the Decepticon cause as an excuse to inflict pain.
The crew of the Lost Light count as well. As someone they meet notes, there's not a sane 'bot among them. Except for Rewind and Rung. Everyone else has at least one thing wrong with them, or a Dark and Troubled Past ready to come back to bite everyone in the ass, or goodness knows what else.
And they get even worse in the second "season", when MEGATRON takes over as captain.
The group in The Transformers: Last Stand of the Wreckers. In general, most Wrecker groups will be this since their roster changes frequently. This is because the Wreckers are a group specifically selected because of their psychological issues with express purpose of throwing them at the worst problems that can be found.
In most versions of The Transformers, the Autobots as a whole tend to be this because they're primarily workers, medics, scientists with no combat experience who had to team up to oppose the Decepticons attempt to subjugate them. Sometimes they've got the benefit of an Old Soldier like Kup or Ironhide who can teach them military techniques from the get go, but sometimes they don't.
The crew of the prototype starship Switchblade Honey is a bunch of screw-ups facing execution (for disobeying immoral, criminal, or just stupid orders from their former superiors) - or, if you prefer, the Only Sane People in a Crapsack Future. And they're humanity's last hope.
In Tomahawk, Tomahawk's Rangers could be viewed as Revolutionary War version of Sgt. Rock's Easy Company. The members included the immensely strong Big Anvil; the dandy Brass Buttons; Cannonball, who was Tomahawk's 2IC; acrobatic French sailor Frenchie; black Combat Medic Healer Randolph; sniper Long Rifle; Stovepipe who was the son of a general and carried a small arsenal in his stovepipe hat; and Wildcat, a Quaker pacifist who turned into a berserker in combat.
The survivors of Wild's End are made up of an ex-Navy man, a reporter, a reclusive writer, a trapper, and a Tagalong Kid.