Just thought of this a moment ago. Dunno if this is already being done or not, if it is then let me know, if it ain't then give your two cents as to why not.
Suppose, to gauge public confusion/contradiction on things like Social Security, foreign policy & whatnot, polls were done where it started off with a short but detailed description of the situation, and then followed with a list of things to do to address that situation and allowed people to pick multiple answers? And then rather than just release the numbers, they ran them by a non-partisan range of experts in that field to analyze what the respondents knew about the situation and/or what they had been convinced about it that was inaccurate or outright nuts? It'd be sort've like a "public awareness" survey, with the aim of finding out not merely what people think but what they know
Also, there could be a takeoff of this that would ask people how best to raise the public profile of the issue, how to get the general public paying attention, thinking, discussing. Asking in effect "what would we have to do to get you to look into this deeper?"
Again, I don't know if this has been done or not, just throwing it out there. If it has been done, then I'd like to be pointed in the direction of an example.