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Dan_Moore comments on The Truth about Scotsmen, or: Dissolving Fallacies - Less Wrong
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The specifics of that are rather beyond the scope of this post (and my understanding.) My point in the second part is that attacking fallacies is a facile and ineffective approach to persuasion because it fails to take into account the other person's state of mind. Fallacies are surface-level manifestations of deeper beliefs, and if you're really trying to convince someone, you have to address the underlying issue, not just the transparent one. It follows that you need to have an accurate model of their mental processes -- that you need to understand not only what they're arguing but why they're arguing it.
Knocking down fallacies is easy and often fun, but it's ultimately just a sport -- effective counterargument requires a more empathetic approach.
Just focusing on the logical issue, and not a strategy for persuasion:
Just because your discussant has a fallacious argument, it doesn't follow that they are wrong. There might be another non-fallacious argument that proves their point.
An analogy: say you find an error in someone's proof of a math theorem. It's possible that an alternate argument can be constructed that avoids that error.