Superhero is always assumed to be a perfect and capable image. Yet, they also have some weakness. Below I just list some of them. Just feel free to add more if you come up with.
Martian Manhunter - Fire
One thing we know for sure is that Martian Manhunter is vulnerable to fire. In fact, it more or less killed him during Final Crisis. There's some disagreement, though, on exactly how the whole thing works. Are all Martians vulnerable to fire? Is J'onn J'onnz just scared of it, like he's Frankenstein's monster or something? Does it simply mess up his telepathy power? Or does it take his powers away? Nobody really knows. Oh, and sometimes he's not vulnerable to it. But then he is again! So, you know, whatever.
The Human Torch - Asbestos
It doesn't get mentioned much anymore, but at one point in time asbestos - that insulating mineral builders used for decades until it was discovered to be a deadly carcinogen - was the Achilles' heel of both Human Torches. They even both had supervillains who used the stuff to fight them. The original Torch had Asbestos Lady, while Johnny Storm had the infinitely goofy Asbestos Man. Of course, we know now that it wouldn't take a superhero to defeat those dastadly villains. Just mesothelioma.
Wolverine - The Muramasa Blade
So there's the sword, right? And it just happens to have been made with part of Wolverine's soul. So, you know, it hurts him. Ruins his healing factor. And, you know, instead of like, locking it up somewhere in some impenetrable chamber where no one can ever get the one sword that could completely kill him, Wolvie just kind of keeps it around, lets Cyclops look after it, whatever. You know, in case he needs it. 'Cause you certainly can't find another sword just lying around somewhere. Better use the one that can really fuck you up in battle, because Lord knows nobody's every taken someone else's sword away from him in a fight!
Green Lantern - Yellow/Wood
The original Golden Age Green Lantern, Alan Scott, can't get wood (I had to do it). His ring's power comes from "green, growing things" or something like that, and so he can't use his powers against them. In particular, wood deflects his powers and makes him look his real age. So watch out for that dresser, Alan! His successor, Hal Jordan couldn't do much against yellow. That's apparently because the emotion(?) connected with the green power rings is willpower while the yellow represents fear. They're opposites, I guess? But if the Green Lanterns "accept fear," they don't have that vulnerability anymore. Sounds easy enough. (Also of note: Alan Scott has yellow in his costume.)
Wonder Woman - Rendered Helpless by a Man Binding Her Bracelets Together
Dr. William Moulton Marston: Creator of Wonder Woman, feminist, guy who thought it was okay to make his creation's weakness the act of being tied up by a man.