This is the best article I've read about the current state of knowledge. We seem to be zeroing on the idea that this virus spreads in bursts, not in a steady manner. In fact, there is mention that there seem to be individuals who, possible for physiological reasons, are especially contagious. Place one of these people in the right setting -- indoors, crowded, loud talking/singing, extended proximity -- and you have a superspreader event.
It's not clear anything about this knowledge would change our strategy. If these especially contagious people exist, we have no way to identify them. And most places have restrictions in place against all that superspreader required behavior.
But it does suggest that the odd protestor refusing to wear a mask in the grocery store is not such a big deal and we could chill about that a bit. (Tyler Cowen suggests we stop moralizing; good luck with that.) Perhaps more importantly, it suggests that is a large element of chance in outbreaks. That is to say, a loud Irish pub could go weeks or months without any trouble, but one superspreader walks in and the whole neighborhood could be infected. That's not a particularly satisfying explanation of the heterogeneity of the epidemic (the data is so contradictory actionable conclusions are rare) but it might be what we got.
The good news is that re-infection looks to be exceedingly rare and possibly only occur in extenuating circumstances.
Herd immunity has not really been found in any documentable way. Every time we think we have found some population that should have achieved it, they have another outbreak. So we can only wait for a vaccine. It also appears the vaccines will have to come from overseas, since we (the U.S.) seem incapable of reducing our onerous standards of safety, despite the urgency of the situation. If there is a lesson from this, it is that we have lost our ability to assess risk in any constructive manner. Maybe everyone should spend more time in Vegas.