The public debate is rife with fallacies, half-lies, evasions of counter-arguments, etc. Many of these are easy to spot for a careful and intelligent reader/viewer - particularly one who is acquainted with the most common logical fallacies and cognitive biases. However, most people arguably often fail to spot them (if they didn't, then these fallacies and half-lies wouldn't be as effective as they are). Blatant lies are often (but not always) recognized as such, but these more subtle forms of argumentative cheating (which I shall use as a catch-all phrase from now on) usually aren't (which is why they are more frequent).
The fact that these forms of argumentative cheating are a) very common and b) usually easy to point out suggests that impartial referees who painstakingly pointed out these errors could do a tremendous amount of good for the standards of the public debate. What I am envisioning is a website like factcheck.org but which would not focus primarily on fact-checking (since, like I said, most politicians are already wary of getting caught out with false statements of fact) but rather on subtler forms of argumentative cheating.
Ideally, the site would go through election debates, influential opinion pieces, etc, more or less line by line, pointing out fallacies, biases, evasions, etc. For the reader who wouldn't want to read all this detailed criticism, the site would also give an overall rating of the level of argumentative cheating (say from 0 to 10) in a particular article, televised debate, etc. Politicians and others could also be given an overall cheating rating, which would be a function of their cheating ratings in individual articles and debates. Like any rating system, this system would serve both to give citizens reliable information of which arguments, which articles, and which people, are to be trusted, and to force politicians and other public figures to argue in a more honest fashion. In other words, it would have both have an information-disseminating function and a socializing function.
How would such a website be set up? An obvious suggestion is to run it as a wiki, where anyone could contribute. Of course, this wiki would have to be very heavily moderated - probably more so than Wikipedia - since people are bound to disagree on whether controversial figures' arguments really are fallacious or not. Presumably you will be forced to banish trolls and political activists on a grand scale, but hopefully this wouldn't be an unsurmountable problem.
I'm thinking that the website should be strongly devoted to neutrality or objectivity, as is Wikipedia. To further this end, it is probably better to give the arguer under evaluation the benefit of the doubt in borderline cases. This would be a way of avoiding endless edit wars and ensure objectivity. Also, it's a way of making the contributors to the site concencrate their efforts on the more outrageous cases of cheating (which there are many of in most political debates and articles, in my view).
The hope is that a website like this would make the public debate transparent to an unprecedented degree. Argumentative cheaters thrive because their arguments aren't properly scrutinized. If light is shone on the public debate, it will become clear who cheats and who doesn't, which will give people strong incentives not to cheat. If people respected the site's neutrality, its objectivity and its integrity, and read what it said, it would in effect become impossible for politicians and others to bullshit the way they do today. This could mark the beginning of the realization of an old dream of philosophers: The End of Bullshit at the hands of systematic criticism. Important names in this venerable tradition include David Hume, Rudolf Carnap and the other logical positivists, and not the least, the guy standing statue outside my room, the "critical rationalist" (an apt name for this enterprise) Karl Popper.
Even though politics is an area where bullshit is perhaps especially common, and one where it does an exceptional degree of harm (e.g. vicious political movements such as Nazism are usually steeped in bullshit) it is also common and harmful in many other areas, such as science, religion, advertising. Ideally critical rationalists should go after bullshit in all areas (as far as possible). My hunch is, though, that it would be a good idea to start off with politics, since it's an area that gets lots of attention and where well-written criticism could have an immediate impact.