The only problem with using advertising is that it costs a lot of money, so nobody buys advertising unless they plan to sell something and make a lot of money doing so. A better approach might be to teach basic critical thinking throughout the curriculum, from childhood to graduate school. Critical thinking can be boiled down as follows:

Whenever anyone makes a claim about anything, he or she should be ready to answer two questions:

(1) "What do you mean by [key concept used]?--the question of CLARIFICATION.

(2) "Why should I believe what you are saying about it?"--the question of JUSTIFICATION.

Thus, for example, you encounter a typical brainwashed Fox Noise addict who makes a claim like "Gun control violates the Second Amendment." You could engage this person by asking,

"What do you mean by 'gun control'? (Since there are many different gradients of this, depending on how you define "gun"). Then ask "why should I believe that it violates the Second Amendment? (when the second amendment is clearly predicated on the initial absolute phrase referring to a "well-regulated militia," not "private citizens.") This of course could lead to a further conversation about what "a well-regulated militia" actually means (i.e. something like the National Guard, in each state, which we already have...)--In short, you've just turned a shouting match into a conversation. And that is why training in critical thinking could be central to overcoming the media saturation of right-wing brainwashing.