I agree that the word intelligence is too vague, but I'm specifically not including a mathematical genius (who would have an exceptional talent in the area of mathematics).
I strongly disagree that average people can't or don't have utilitarian inclinations. I think utilitarianism is one of the easiest philosophies to grasp, and I know a lot of average-IQ people who express the desire to "do as much good as possible" or "help as many people as possible." Even the advertisements for charities that you mention tend to stress how much good can be achieved with how little money.
It's certainly good to customize advice, but I think there is a class of advice I would offer to smart, skeptical people that I would hesitate to give to others. For example, I would tell my brightest students to question expert advice, because then they can more deeply understand why experts think what they do, or potentially uncover a true fault in expert reasoning. With my less-bright pupils, I find that this pushes towards conspiracy theories and pseudoscience, and thus more frequently advise them to trust experts and distrust people on the fringe. When smart people question mainstream scientific thinking, they may go astray. In my experience, when average-or-below intelligence people question mainstream scientific thinking, they almost always go astray, and when they don't it's usually coincidence.
I'm trying to figure out how to help them understand things more deeply and question things in a more productive manner, and definitely borrowing lots of ideas from LW, but I still think there is a lot more room for improvement.
I know a lot of average-IQ people who express the desire to "do as much good as possible" or "help as many people as possible.
I'm sure they express the desire, but do they actually desire it and do they actually do it?
What should a not-very-smart person do? Suppose you know a not-very-smart person (around or below average intelligence). S/he read about rationality, has utilitarian inclinations, and wants to make the world better. However, s/he isn't smart enough to discover new knowledge in most fields, or contribute very much to a conversation of more knowledgeable experts on a given topic. Let's assume s/he has no exceptional talents in any area.
How do you think a person like that could best use his/her time and energy? What would you tell the person to do? This person may be, compared to average LW readership, less capable of noticing the irrationality in his/her actions even if s/he wants to be rid of it, and less easily able to notice the flaws in a bad argument. S/he may never be able to deeply understand why certain arguments are correct, certain scientific facts have to be the way they are, and telling him/her to be unsure or sure about anything seems dangerous if s/he doesn't really understand why.
My practical advice might be:
1) If you want to give to charity, follow GiveWell recommendations.
2) Learn about the basic biases, and commit to resisting them in your own life.
3) Follow advice that has been tested, that correctly predicts a positive outcome. If a hypothesis is untestable (there's an unsensible dragon in your garage) or doesn't predict anything (fire comes from phlogiston in combustable substances), or is tested and demonstrably false (god will smite you if you say it doesn't exist), don't waste time and energy on it. If you want to improve, look for tested methods that have significant positive results relevant to the area of interest. Similarly, if a person regularly gives you advice that does not lead to good outcomes, stop following it, and if someone gives advice that leads to good outcomes, start paying attention even if you like that person less.
At a more general level, my thoughts are tentative, but might include basic LW tenets such as:
1) Don't be afraid of the truth, because you're already enduring it.
2) If all the experts in a field agree on something, they might be wrong, but you are extremely unlikely to be better at uncovering the truth, so follow their advice, which might appear to conflict with...
3) Don't trust deep wisdom. Use Occam's razor, think about simple, basic reasons something might be true (this seems good for religion and moral issues, bad for scientific ideas and understanding)
4) If you find yourself flinching away from an idea, notice that, and give it extra attention.
Note: I mean this as a serious, and hopefully non-insulting question. Most people are intellectually near-average or below-average, and I have not seen extensive discussion on how to help them lead happier lives that make the world a better place.