If you could impart to the general public a handful of insights, in or about philosophy, what would they be?
A few ideas that spring to mind:
1) Philosophy (and that includes ethics!) isn't just a matter of opinion. Some opinions are better justified, or more reasonable, than others. We should aim to hold those judgments that are best supported by reasons.
2) Philosophy is a form of inquiry, not rhetoric or apologetics. One should be open to the possibility of changing one's mind, and - ideally - view opposing arguments as opportunities for learning, rather than threats to be dismissed at all costs.
Corollary: The aim of argument is not to convince others to your point of view regardless of its true merits, but rather to adduce rational evidence that the view is most likely correct, i.e. true.
3) The idea of objective truth is nothing to be scared of, and shouldn't lead to dogmatism so long as we recognize our own fallibility. Just because the truth is out there, doesn't mean we have a perfect grasp of it! If anything, it's relativism that leads to dogmatism, since the relativist holds that merely believing something suffices to make it "true for you". That would mean that you cannot possibly be wrong, so self-doubt or rational reflection is rendered superfluous.
Corollary: those who take seriously the dictum 'live and let live' should understand tolerance to be an objective value. Otherwise, intolerant authoritarians aren't really doing anything wrong. They're merely going against your arbitrary liberal preferences. "No big deal."
4) Moral facts are not reducible to the dictates of any authority. If God, society, and the individual, all approved of torturing animals for fun, that wouldn't suffice to make it right. This immediately refutes all those idiotic theories (e.g. Divine Command theory, cultural relativism, egoistic subjectivism) which reduce morality to an arbitrary subset of preferences. (What really matters is minimizing harm and promoting flourishing.)
Corollary 1: the widespread belief in a connection between religion and morality is rank stupidity. (And the idea that God could assign your life a "meaning" is no less silly.)
Corollary 2: Just because you find something "icky" doesn't mean it's immoral.
5) We can provide non-spooky natural foundations for morality. Presumably facts about welfare, i.e. what harms or benefits an individual, are naturalistic. And, just as plausibly, the moral facts are entailed by the facts about everyone's welfare (including sentient non-humans). It's axiomatic that it's good to benefit people, bad to harm them, etc. Nothing especially mysterious or supernatural is going on here.
6) God probably doesn't exist. The God Hypothesis doesn't fit well with observed reality. (The only argument I've ever come across that warrants much respect is the cosmological fine-tuning argument. The others are just shockingly bad.) No, we can't prove the boogeyman's non-existence with absolute certainty, but nor do we need to. And no, religious hallucinations aren't good evidence.
Incidentally, sending honest non-believers to hell is evil. It's scary how many people exhibit moral blindness with respect to this belief. Worshipping an evil deity reflects poorly on one's own moral compass, I should think.
7) Time doesn't move.
8) Either this sentence is false or self-referential paradoxes are great fun.
9) Taxation is not (necessarily) theft. The common right-wing slogan rests on superficial and sloppy thinking.
10) Any form of freedom worth having requires more than mere non-interference. Recognizing the political goal of Enabling Humanity is independent of any particular suggestions for how to achieve it, but on the latter point I think there's a great deal to be said in favour of an unconditional basic income.