He's the man. The villain has been vanquished, the innocent protected, the world saved yet again, often at the very last moment. If it had been anyone else, it's the Big Damn Heroes moment. Only someone forgot to tell the Big Damn Hero.
Inspector Oblivious isn't aware he vanquished evil, protected the innocent or saved the world because he's in one of his own. He's doing his own thing not recognizing the screaming coming from the cat-stroking archvillain who waves one fist angrily at the monitor as yet another plan is foiled and yet more minions are carted off to jail (or the morgue). It wouldn't be so bad if it was intentional, if he was facing an adversary worthy of their battle, but the hero is a complete doofus who's proud because he thinks he foiled a scheme to illegally sell fake Girl Scout cookies, ignoring the orbital Death Ray satellite plunging into the villain's volcano headquarters that resulted from Inspector Oblivious's pratfalls, mistakes and cluelessness. And he does it again and again.
Some days an Evil Overlord just can't catch a break.
- Detective First Class Mihoshi Kuramitsu is all but the textbook example. Her more than distinguished record in the Galactic Police is much more due to her bumbling unraveling all and any evil plans and sheer blind luck than any actual competence. At least in some versions, she also has an unfocused sort of Hyper-Awareness that results in her reports containing heaps of valuable information, most of which she never realised the significance of.
- Irresponsible Captain Tylor: Captain Justy Ueki Tylor — maybe.
- Deadpool: P.I. Wade is trying to solve a murder, and he's so oblivious that he forgot HE was the one who killed the guy in the first place.
- Inspector Jacques Clouseau is capable of solving cases and in one film even saving the world through his cluelessness. He is a Walking Disaster Area of such caliber that he was the very reason the world was in danger to begin with, though...
- The James Bond parody in Casino Royale (1967) has a whole cast of James Bonds (It Makes Sense in Context — British Intelligence gave all of its agents (even the women) this name in an attempt at distraction) collectively demolishing a criminal scheme through sheer bumbling. None of them make it out alive -- at least they took the villain with them.
- The plot behind The Man Who Knew Too Little, who believes he's in modern experimental play when in fact he's been mistaken for a spy and ends up disarming a bomb to Russian music in a middle of a embassy. Oh! While dancing, of course.
- PC Wodehouse's Ashe is an author trapped in a contract to write serials about the Detective Gridley Quayle, whom he describes as "so maddeningly blind to the fact that only the most amazing luck enabled him to detect anything." Just like Ashe.
- The original inspiration (and voice!) for Inspector Gadget, Maxwell Smart.
- Sergeant Frank Drebin, Detective Lieutenant Police Squad!. Yet another. He takes on this character type more in The Naked Gun series than in Police Squad!. If anything, in Police Squad! he is ridiculously competent and is a talented comedian, basketball player, brawler, agent, boxing coach, etc. (That list might have continued to grow if the show had not been canceled so soon.)
- Inspector Gadget, whom we honour for unintentionally saving the day.
- Phineas and Ferb: If you consider Candace as 'evil' for trying to get them into trouble, Dr. Doofenschmirtz falls into this trope. He has only occasionally come into close contact with the boys, but his inventions inevitably get them out of trouble.