Something ideological opposites can agree on

If there is one thing that people of the most opposite political opinions can agree on, it is that an alarming number of people are wrong about the plain facts regarding very important issues.

It may sound like a joke to call this a shared concern, when each side is pointing accusingly at the other's wrongheadedness, but is there any way to turn this agreement into a movement or project to raise our national "Truth Quotient"?
In such a polarized political world it seems that nothing one side says can influence how the other side thinks about anything.  I would like to envision a state of affairs where a conservative could point out a flaw in a liberal program, seen as a flaw by both sides once it is carefully examined, and the result is an improvement in the eyes of both liberals and conservatives.

Are there things we could focus on that should bring us as a whole closer to the truth about some things - bypassing for the moment those on which we most violently disagree?  In war it is fine for
 
  One general may adopt the policy that the less truth the other side's general understands, the better, but does this work for two parties in a democracy?

Can we find examples where divided groups have found methods or procedures to increase the odds of taking the decision that appears best in view of the truth?  Well functioning legislative and judicial bodies might have something to teach us.  Courts have court reporters and Congress has its Congressional Record (and of course there are recordings and videos).  When members want to know what was said, they go the these, rather than to their favourite partisan "news" source.

Suppose we could agree to cooperate to ascertain, refine, and make highly accessible only the most straightforward and unequivocal facts, and designate some non-partisan body to guard this central resource.

It is good for academics to continue the ongoing dialogue on epistemology, and some of that work is very good, but I'm not holding my breath for that work to escape the ivory towers, and go viral in the world (and contribute to our salvation in case we need salvation).  I'm not saying it won't, and if I can help bring that about, I'd be very happy.