The funny thing is, I don't think these moments are necessarily all that bad an idea, as they give Superman such a concrete personality.
I agree with you: there's a clear appeal to seeing Superman as a fallible character, even one bordering on the psychotic. His world and situation are completely insane, when you think of it. He is a serial liar who spends half his time pretending to be someone else, he is secretive to a degree that might be diagnosed as paranoid, or at the very least severely depressed. It's almost reassuring to see him fail in these ways.
What's interesting, though, especially in the 1950s stories, is the fact that just about everyone behaves in this way, as if the entire world were bipolar (which, in some ways, it was back then). Lois goes to extraordinary lengths to weasel out Superman's secrets, Perry wants impossible stories, Jimmy hoards Superman memorabilia. The general public is frequently portrayed as craven, money-driven and emotionally stunted - I remember a story in which some inventor perfects a machine that erases people's memories (I thought at first it was the one referred to by MatterEaterLad above, but it's not that one), and people go mad for it, everyone having guilt or grief that they want rubbed out.