Jeff Cooper demonstrates why I have him on my regular reads by giving the perfect example of why fisking is pointless.
Jeff also makes a good point that the technique (preferably without the name fisking) can be useful. I would point out it is very useful when used to combat creationists and others who make a wide number of unsupportable claims in a minimal amount of writing. talk.origins is full of such examples largely because creationists tend to lie, misrepresent, or simply are too confused to know what they are talking about. In that case, the only effective way to discredit their writing is to take each minute claim apart.
In most articles there is a structure. Attention getter/introduction, thesis, supporting evidence and conclusion. Taking apart a single sentence away from that structure is often either pedantic or a misrepresenation of the actual point. Somewhere around 6th grade most people learn that they make a point with a paragraph, not a sentence.