Personally, having rejected the idolization of general intelligence (yes, I.Q.) as inhumane and unfair, I think most of the folks in this thread are coming at the idea of stupidity from a biased, unnecessarily political standpoint. Even testing based on mathematical, geographical, or tradeskill knowledge is misguided (as are many tests students take), because in the testing there is no reason to assume a desire for that knowledge. As has been pointed out, having the right answer to a test can be cheated, faked, or bought in any number of ways. Whether in the classroom or in the death-ray voting booth, tests have a fatal flaw: they don’t care whether the answerer wants to know anything on which they’re reporting.
Eliminating taxes on books, especially non-fiction, is a good start, but you’ll still have people who only seek out the opinions of those with whom they already know they’ll agree. This is where most of the dangerous and addictive stupidity lies in modern society: people don’t desire to form their own opinions because they have newsanchors, editors, and bloggers who can gather, analyze, and wax poetic on the information in their stead, and all the layman has to do is consume it.
Stupidity is not ignorance of a certain genre of knowledge. Stupidity is the absence of a desire for knowledge and the motivation to critically examine it in the context of one’s world.
As dropzone mentioned upthread, people these days are no longer limited to talking to people in their own town, which is why it seems like there’s more stupid-itis going around. This works both ways, however: when people can only communicate in small groups, the desire for knowledge (at least for local knowledge) is a thirst that can’t be quenched. Knowledge solves problems and critical thought gives new insight to old problems. Before the internet and information-aggregators, knowledge and the ability to use it was a rare and beautiful thing, even if it was far more limited in scope and accuracy. Nowadays, any subject such as horse-riding grandmastery appears from the ground level to contain too much information for any one person to sift through–and why bother? horsemastah.blogspot has already done most of the work, even if he may have left out the histories of pro-feminist horses due to an unspoken political bias.
What I mean is: it’s too attractive for people to spend time consuming someone else’s opinion rather than spending more time to form their own. What this leads to is a) opinions based on ignorance of how the world works, b) politicians out of touch with their constituents, and c) a blind trust for anything said on one’s own favorite news networks.
And there are reasons for Joe Sixplumber and his extended family to know where Iraq is on a map. Even the most noble Joe, a family man with interior defense on the brain, ready to volunteer to be shipped out wherever his country needs him, should be aware that Iraq is right next to Syria and a lot of other countries where the culture and history includes a lot of reason to hate the U.S. and, by extension, U.S. troops. Joe Sixprivate might like to know this intimately before he ships off, but not knowing it is his own onus.
Joe Sixhawk, however, who will vote all day to “glass the bastards!” without knowing any of the history or danger into which he’s voting to put his own fellow citizens while spending their tax money - he actually has an obligation on behalf of both the volunteer military and the politicians whose opinions he can sway by having a voice to learn what the fuck it means to invade a place like Iraq, so an informed and fair and balanced decision can be made on whether it’s a good thing to lobby for and support.
(But now that I’ve gone and blown my careful cover about my own liberal bias, I’d like to share an anecdote to respond to my esteemed colleague Sam Stone. In high school I had the option to take any number of vocational classes that would have helped better me as a person. If I’d taken Car Machinery, then I’d have gotten easy credit hours for learning how to change my own oil and troubleshoot my engine. Unfortunately, I already had a lot of run-ins with the types of folks who filled those classes, and those were the types who may’ve liked to take advantage of the loud, cramped quarters of a garage to get easy credit hours for learning how to beat the hell out of a faggot, rather than just doing it between classes. Make of this what you will, but don’t pretend - as chappula has - that most good ol’ boys in the South will treat you politely in a discussion if they think your views on religion and politics differ from theirs. Mandatory service on a farm is just as bad as mandatory knowledge of quantum physics, but one of those types of knowledge can usually be gained without the risk of encountering the type of person whose knuckles itch when they see a guy wearing a suit outside of church.)
Now that that’s out of the way 
The only concrete solutions I can think of for getting people to trust their own brains rather than the brains of John Stewart or Rush Limbaugh are either to deregulate the airwaves so that it becomes a mess of uninformed opinions and people have to scrounge for unbiased news, thus weeding out unreliable sources and once again acquiring a healthy skepticism for what they hear; or offering a sweepstakes after every news broadcast that can be entered by anyone who sends in evidence of factual errors or overly biased selectiveness/language in the broadcast. It would need to be a random drawing, so people would avoid making cheat-sheets of relevant counterfacts (until after the drawing, since those cheat-sheets would be quite informative) and thus becoming a second strata of opinionmonger. The sweepstakes could be sponsored by the government or a rival news network, though that would just encourage bizarre opinions to bankrupt one’s opponents. Or we could go balls-to-the-Berlin-wall and just have the government force political opinionmongers in the U.S. to cough up money for the sweepstakes themselves, as long as they’re, say, folks who make over half of their income by broadcasting their opinion on global news and politics and they make over a few million per year total.
So err, the details need some working out. But, in short, I think the way to get people to think more is to discourage the influence of political jockeys so more folks have to go to smaller sources (whether bloggers or the AP) to fit the pieces of information together.
Now, where’s that endless taco bar?! 