Martian Manhunter is considered the "Superman" type character of the JLA whenever Supes isn't around. He's strong, can fly, walks through walls, can change shape, and is really smart. He's from Mars, and oh yeah, he's dropped by fire.
Fire! Why? What is it about fire that can drop this super-alien? It's never been explained away.
So picture this: an apartment building is on fire and suddenly you see this blue streak blazing toward you. You're saved! Nope, it's the green guy who can lift buildings, walk through walls, and change shape...you are officially dead mean unless Batman's in the area.
Appreciating the fact that lead flying from the barrel of a gun can kill just about anyone, you would think that someone with Superman's powerset would be impervious to bullets. Not so with Mon-El.
This poor soul can't stop a robbery in progress unless they are brandishing knives or ray guns. Imagine that, you spend all your money on the latest technological weapons, and someone finally does him in with a .38.
He's recently come back to the DC universe and helped Superman for a while during Supes' absence, but the fact remains he started out with being helpless and pretty much useless for a while.
3. Your Own Name
If you're looking for stupid weaknesses, I honestly can't think of one any worse than this.
You swoop in, save the day, stop the supervillain, and when folks ask you who you are, you can't answer them without turning into a normal guy again. Too stupid to be true? Nope, that's Captain Marvel Jr.
He may have stepped into the role of Shazam and become the true Captain Marvel now, but there for a while you have to admit it sucked for him. Why he didn't choose a different name, I'll never know. Why screaming "Captain Marvel" changed him while the rest of the Marvel family yelled "Shazam!" I'll never know. It just all added up to a rather strange dilemma for the guy.
I know this one doesn't count anymore, but for a while there this one was a problem for Alan Scott, the original Green Lantern. I never understood why the color yellow messed up Hal Jordan, but wood just doesn't make sense at all.
In a much later story, they revealed that Scott's weakness to wood was psychological because he got knocked on the head during his first outing and gave himself the weakness.
I also know the Green Lantern Corps are no longer weak to yellow, but think about this: for a while you could have defeated every Green Lantern out there (including Alan Scott) with a yellow baseball bat. Scary!
You are the Devourer of Worlds. You hold the Power Cosmic. You are gigantic. And you are always hungry!
Galactus has to constantly go from planet to planet, eating them as he goes along. If he doesn't find a suitable one in time, he will starve to death and die.
So here's the big question: what happens when he finally eats all the suitable planets in the universe? So, in essence, he's actually killing himself with every planet he eats.
Comic books...you gotta love 'em!