Probably the question of Multiverse- versus Collapse-Interpretation in Quantum Physics could suffice. It fits your needs as a factual and, somewhat, important question, while there is no overall aggreement in the respective fields of experts (although the trend to MI seems becoming clear...). Furthermore I guess there aren't any status- or mindkilling-issues concerning this question, but, and that might rule out this question at least in some cases, a religious person might feel otherwise and reject the idea of "multiple creations" at first sight. Regarding "High uncertainty" the MI/CI-conflict might not fit your scheme, as(you already know if you read the Quantum-Physics-Sequence) there is a strong Bayesian argument to decide for Multiverse-Interpretation, but since you are going to talk to people who don't know about expressing their believes in probability, they maybe will not have read into that topic either (of course this just describes the standart-street-guy you encounter, maybe not you discussio-club-friends...). If so, at their state of special knowledge, there is little reason to value one more than the other. The worst would be for them to consider this a problem plainly boring or - within high physics- out of their reach, but if you explain multiverse beautifully enough and, maybe, ask them to imagine they are supposed to discuss the topic in a school-essay, it could become interesting enough.
But in order for them to even give a meaningful probability estimate, they'll need to spend years actually studying the relevant physics and mathematics. It doesn't matter how eloquently you explain MW - the Universe doesn't run on rhetoric.
If you ask people about MW versus CI, from their perspective it's no different from asking "does the glibbleflop spriel or does it just florl?"
When I explain to people how beliefs should be expressed in probabilities, I would like to use an example like "Consider X. Lots of intelligent people believe X, but lots of equally intelligent people believe not-X. It would be ridiculous to say you are 100% sure either way, so even if you have a strong opinion about X, you should express your belief as a probability."
Trouble is, I'm having a hard time thinking of an example to plug into X. For an example to work, it would need the following properties:
Factual question. So no value-laden questions like "Is abortion morally acceptable?" or counterfactual questions like "Would the US have won a war with the Soviet Union in 1960?"
Popular and important question. The average person should be aware it's an issue and care about the answer. So no "My aunt's middle name is Gladys" or "P = NP."
High uncertainty. Reasonable people should be reluctant to give a probability >90% or <10%
No opportunity to gain status by signaling overwhelming support for one side. So cryonics is out, because it's too easy to say "That's stupid, I'm 100% sure cryonics won't work and no intelligent person could believe it." I'm assuming in any debate where you can gain free status by assigning crazy high probabilities to the "responsible" position, people will do just that - so no psi effects, Kennedy assassination, or anything in that cluster. I need a question with no well-accepted "responsible" position.
Minimal mindkilling effect. My previous go-to example has been global warming, but I keep encountering people who say that global warming 100% for sure exists and the only people who could possibly doubt it are oil company shills. Or if I were to try the existence of God, I predict half the population would say it's 100% certain God exists, and the other half would say the opposite.
So what are the important questions that average (or somewhat-above-average) people will likely agree are complicated open questions where both sides have good points? And if there aren't many such questions, what does that say about us?