The Elephant in the Room spends a livejournal post talking about things that don't make sense when it comes to Superman. His reasons: (1) He can't die, thus no tension (2) Kryptonite makes no sense (3) The costume is silly (4) He doesn't solve real world problems (5) the disguise as Clark Kent is flimsy at bst. The comments indicate that he's not alone.
There's an essay in The Man from Krypton (ed. Glenn Yeffeth) called "Six Things that Plain Don't Make Sense about Superman," published in 2005. That essay lists (1) The Pathetic Inferiority complex of the Kandorians, (2) The Frightening Destructive Potential of Superbaby (3) The Odd Construction of buildings in Metropolsi (4) The odd favoritism demonstrated by Jimmy Olson's signal watch (5) Street level thugs who honestly believe they stand a chance, and (6) The absence of any real world limitations to superhearing.
In other links, here's the solution to the mystery of Superman and the Cyclops.
This one's pretty interesting. It's about how Superman can be boiled down to the description: A police reporter affects the outcome of the crimes he covers, then writes about them, hiding his involvement. (from the same website: who should write superman)
I've seen the story of Superman boiled down to one theme on several occasions. Josepha Sherman distills it to either the moses story (baby set adrift, found and rasied, becomes hero) or the story of a hero learning his heritage--these both in her book Once Upon a Galaxy.
Then there's the discussion between Tim Callahan and Steven Withrow in Callahan's column When Worlds Collide. They go over superheroes as "archetypes". This bit by Callahan is interesting, in response to Withrow calling Batman "the dark knight detective" as if it sums up his character.
But doesn't Batman represent something more primal? The "dark knight detective" aspect is something that comes out of Batman's pulp roots perhaps, but isn't he more like "the god of problem solving"? And he mostly ends up solving the problems by punching them in the face, no matter how much his intellect, planning, or Bat-computer might help him get to that point.
Superman, in many ways the opposite, doesn't have any problems, except those which he manufactures for himself. He could correct any injustice almost instantly, and even the social problems writers saddled him with for years were mostly the result of his attempt to pretend at humanity. To pretend to have those very problems. Had this mythic character never adopted the guise of an awkward newspaper man, he wouldn't have had to trick Lois Lane all those times. And he wouldn't have had any of those dual-identity struggles. Batman punches problems in the face to become superhuman, while Superman creates problems for himself to become human.
Does that mean that it's not just Superman that was necessary to birth the superhero genre, but the duality between Superman and Batman?
Withrow doesn't agree with that last point: But I still think the Batman archetype is a reaction against the Superman archetype. Not simply because Superman came first, but because I believe the world view that underlies Superman is more fundamental to human nature than the world view underlying Batman. We are born with a yearning for Superman as our ideal and must learn (if we ever do) to accept Batman as our reality.
I'd like to draw the parallel here with a comment I quoted not long ago, made by Josh Walgenbach: Batman is a man trying to be a god. Superman is a god trying to be a man.
In the 1970's, writer Denny O'Neil produced a new take on Superman, one that was significantly less powerful and more connected to humanity. Here's a lengthy overview, with lots of scanned pages, of that run.
That about does it for now.