So what if every American, during their public school years, were required to take (1) some basic linguistics, and (2) classes teaching comprehension of all the major dialects of English (ideally in addition to a foreign language of their choice)?
I'm not suggesting that they study advanced phonological or syntactic theory, especially not in elementary school. However, many of the most important lessons in an introductory linguistics class — for instance, the idea that there is no one right way to speak, and that languages change, and that the boundaries between one language and another are never as clear-cut as one might hope — are also important lessons when generalized to life. And it wouldn't hurt their problem solving skills either.
In a similar vein, recent events (such as the George Zimmerman trial, which also made painfully clear the extent to which an individual's dialect influences their perceived intelligence) have shown that Americans — especially speakers of the major prestige dialect of English — have a hard time understanding unfamiliar dialects of English. This is almost certainly due primarily to lack of exposure; that could be fixed by explicitly teaching all public school students, ideally from a young age, to understand (and speak; you'd probably have to teach speaking to effectively teach understanding) the dialects in which they are not native. Such a program would also level the playing field for native speakers of non-prestige dialects, who currently have to pick up the prestige dialect on their own, often after growing up with little or no exposure to that dialect.