Even Arguments based on false premises can be sound. Just as arguments can be based on true premises and still be unsound. Helping people identify which is which should at least raise the quality of disagreements.
When its premises are false, an argument is always unsound. But it can still be valid. A sound argument is one that is both valid and has true premises.
About builiding a soundness/validity graph, I've dabbled with building a webapp for that (though the graph is more implied than visual). It's still very basic, but if someone has ideas where exactly it should go or how it could be engaging to a community of critical thinkers, please contact me.