Of course, it's not just the psi powers that can muddy the waters. In Heinlein's "Gulf" we're presented with "Speedtalk," a language that follows the principles of General Semantics and makes your thinking better because, um, well, because General Semantics is so cool.
That leads us to another problem with the stories of the supersmart. Once given the gift of supersmartness, the protagonists often come around to various views, opinions, and theories that happen to coincide with either the author, John. W. Campbell Jr., or the average Analog reader, depending. Often it's all three, at least in a certain (and obvious) category of story. But one should also bear in mind the case of the translation of "Flowers for Algernon" to the big screen, where Sterling Silliphant's screenplay inserted all sorts of cliché's of mid-60s liberalism into Charlie's dialog.
The real difficulty is that it's very hard to write convincingly about someone who is smarter than you, and it's really, really hard to write convincingly about someone who is smarter than anyone who ever lived.
So there are various cheats. One cheat is to mash together all the tales of mental prodigies into one package. Good Will Hunting was one such. Math genius, plus eidetic memory, plus (apparently) total logical comprehension of everything he read, so he could put down a college student for just regurgitating his textbooks, without himself just regurgitating some more textbooks.
Also, he was really good in a bar fight.
There's a similar problem with the TV show, Numb3rs, where Charlie Eppes is a math genius (and former prodigy) who uses mathematics in all sorts of crime-solving ways. The show's advisors do a decent job of making the math realistic, but what they can't do is make it realistic that one single mathematician would be an expert in so many areas of applied math, all the more so because he was a math prodigy, and math prodigies tend not to be in the applied areas, but rather in things like number theory.
The focus of the supermind story is also important. Often the focus is on the genius' relationship to society and the people around him, so it's often an extrapolation of the gifted or geeky readers' experiences. One important question is whether or not the story offers some useful lessons to said gifted geek.
I remember being struck by one passage in George O. Smith's The Fourth R (which turns out to be available from the Project Gutenberg, imagine my delight). A wise old man named Judge Carver is speaking to the protagonist, who's been artificially given a full adult's education by a "brain machine":
"Let's take the statistics first. You're four-feet eleven-inches tall, you weigh one-hundred and three pounds, and you're a few weeks over fourteen. I suppose you know that you've still got one more spurt of growth, sometimes known as the post-puberty-growth. You'll probably put on another foot in the next couple of years, spread out a bit across the shoulders, and that fuzz on your face will become a collection of bristles. I suppose you think that any man in this room can handle you simply because we're all larger than you are? Possibly true, and one of the reasons why we can't give you a ticket and let you proclaim yourself an adult. You can't carry the weight. But this isn't all. Your muscles and your bones aren't yet in equilibrium. I could find a man of age thirty who weighed one-oh-three and stood four-eleven. He could pick you up and spin you like a top on his forefinger just because his bones match his muscles nicely, and his nervous system and brain have had experience in driving the body he's living in."
"Could be, but what has all this to do with me? It does not affect the fact that I've been getting along in life."
"You get along. It isn't enough to 'get along.' You've got to have judgment. You claim judgment, but still you realize that you can't handle your own machine. You can't even come to an equitable choice in selecting some agency to handle your machine. You can't decide upon a good outlet. You believe that proclaiming your legal competence will provide you with some mysterious protection against the wolves and thieves and ruthless men with political ambition--that this ruling will permit you to keep it to yourself until you decide that it is time to release it. You still want to hide. You want to use it until you are so far above and beyond the rest of the world that they can't catch up, once you give it to everybody. You now object to my plans and programs, still not knowing whether I intend to use it for good or for evil--and juvenile that you are, it must be good or evil and cannot be an in-between shade of gray. Men are heroes or villains to you; but I must say with some reluctance that the biggest crooks that ever held public office still passed laws that were beneficial to their people. There is the area in which you lack judgment, James. There and in your blindness."
"Blindness," repeated Judge Carter. "As Mark Twain once said, 'When I was seventeen, I was ashamed at the ignorance of my father, but by the time I was twenty-one I was amazed to discover how much the old man had learned in four short years!' Confound it, James, you don't yet realize that there are a lot of things in life that you can't even know about until you've lived through them. You're blind here, even though your life has been a solid case of encounter with unexpected experiences, one after the other as you grew. Oh, you're smart enough to know that you've got to top the next hill as soon as you've climbed this one, but you're not smart enough to realize that the next hill merely hides the one beyond, and that there are still higher hills beyond that stretching to the end of the road for you--and that when you've finally reached the end of your own road there will be more distant hills to climb for the folks that follow you."
Mickey Spillane did a similar turn in a book called The Twisted Thing, but he had the gizmo make the young boy into, mentally, a real adult, supersmart, but still locked inside the body of a boy. It's a horror study really, and doesn't end well. But what caught my attention in that one is that the supermind notes that Mike Hammer, not really the brightest guy in the world, manages to almost keep up, owing to the fact that Hammer is a specialist in criminal matters, and specialization allows lesser talents to equal or even surpass greater ones who cannot specialize in everything.
These are real lessons, and not just applicable to someone who is supersmart, but even to us folks who are middling to very smart. And ultimately, it's a lot better to pull such lessons from wish-fulfillment fantasies than such panderings as "they're just jealous of your intelligence" and "if everyone were really smart, they'd agree with you about stuff."