There are only two places that an arguement can be wrong. Either the premises used to support a conclusion are not true - or the conclusion does not follow from the premises.
That's it. That's the only two places you need look when addressing a claim. Once you understand this basic prinicple of logic it makes seeing the logical fallacies of politicians, and everyone else, infinitely easier.
To your point Phizzy, the only time someone could make a "good argument when they're wrong" is if we were operating under false premises that we believed to be true. Though, once the premise was discovered to be false or not supportable, the wrong argument would cease to be a "good" argument.