Discussions among Superman fans tend to come down to disagreements over a handful of key issues.
Political vs Apolitical
Should Superman be an agent of change actively working to fix the problems of human society or should be super-powered 911 there to help when we get in trouble. I think there's decent arguments to be made on both sides of this debate, and I think this conflict should be a major part of the character.
His relationship with Lois Lane
Does she know he's Superman? Doesn't she know? Are they married? Honestly, I think you can tell great stories with any of these status quos, and I'd like to see more variety in this regard.
The portrayal of Clark Kent
Is he a bumbling nerd or simply Superman with glasses? This really comes down to Reeves vs Reeve. I tend to favor the idea that Clark is more of an exaggerated persona because it's very funny to me, but I understand that some readers want to see Clark treated more seriously. Both versions work just fine, but one feels like wasted potential. The Clark Kent of George Reeves, Dean Cain and Henry Cavill are indistinguishable from Superman. I'd rather they have more fun with it.
Superboy vs Superman
I think history has shown that if you want to have a Legion of Super-Heroes, you can't remove Superboy from his history, but I very much appreciate the thinking that Superman's arrival into the public eye should not be preceded by the exact same thing, only younger. I think the best way to handle this is making his adventures as a kid a clandestine thing and keep his costumed adventures as Superboy in the 30th Century.
Meeting Lex in Smallville or Metropolis
There's pretty good arguments to be made on both sides of this one, too. However, I think the current idea of having Lex in Smallville, but not as a friend of Clark's is a complete waste. Why bother having him in Smallville if you aren't going to have them be friends. What is the value to having them share a hometown?
Ma & Pa Kent's survival
While I can respect those that want the Kents around for Clark to head back to whenever he needs advice or apple pie, I think they are largely redundant once he becomes Superman and reveals his identity to Lois, who then becomes his primary confidant. I think they should have split the difference and kept Ma alive with Pa dead, but I'm curious to see if any worthwhile stories come out of their latest resurrection.
The destruction of Krypton and who survived
I prefer the ultimate cause of Krypton's demise to be the result of hubris, rather than malice, but I don't really care what the cause is as long as Krypton is dead and the number of survivors is limited to Superman, Supergirl, Krypto, the Phantom Zone Criminals, and whatever the population is in the Bottled City of Kandor. They tried limiting it to only Superman post-Crisis and all it led to was convoluted nonsense that satisfied no one.
Anything else I missed?