Interesting responses so far. My idea is kind of out there, since it doesn't directly address a lot of the more urgent issues going on today but would have a good shot at affecting things 20 years down the line.
Reform the public education system so that it's federally funded and includes logic as one of its major subjects. Since many history and social studies programs are manipulated specifically to discourage discourse, this subject could be replaced by logic, or the two could be fused (however the latter comes at a risk of a politically motivated curriculum.)
The reasoning here is twofold. First, I have a very strong belief that racism and class inequality stem from inequality in education, especially in grade school. Federal funding would level the playing field for low-income households in a more substantial way than welfare or affirmative action (which are decent, but really just mask the symptoms of a larger issue.) A better education for these people would mean better chances of landing a better position and ultimately cause slums, along with their respective problems of drugs and crime, to shrink.
Teaching logic is something for which my reasoning is slightly more indirect. Lobbying is the biggest thorn in America's side right now, but I think that problem (among others) was allowed to get as bad as it was due to peoples' ignorance. Logical fallacies are quantifiable and demonstrable chinks in major political positions, and I think if they were a part of the cultural lexicon, representatives would have to run on more policy-driven campaigns.
That being said, a big issue with the federal government is that people aren't taking enough responsibility for their local government, and it's local representatives that need to be replaced before we can start seeing decent candidates running for federal positions. There's also no guarantee just teaching logic would allow people to connect the dots between deregulation and lobbying.
The reason my opinion stands is that teaching logic should, in essence, make people more willing to reconsider positions that are supported by good evidence. Seeing lobbying for what it is, the causal relationship between local and federal elections, and cutting out distractions should generally be easier when people take an x-ray to political beliefs that are flat-out wrong. Again, this doesn't necessarily stamp out evidence that has actually been tampered with (usually by publication bias) but I think it's a good start.
Side note, if anyone DOES know how to fight publication bias, the sensationalism of strong headlines over nuance, or the tendency for common sayings to be short and catchy rather than well-supported and nuanced, these would be massive, long-term improvements to society as well.