It is quite common in comments about major news stories, especially if it's about a crime. Someone disproves a very tiny detail, possibly a mistake of the news-writer, and claims that thus the whole story is disproven. Usually it follows with a rant about how we are all misled by the powers above, and they falsely accused this innocent person, etc., but in reality the event really did happen, and the false detail was quite unimportant.
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1Look up the fallacy of composition. What you're describing is the negative form of this. – Robusto Aug 3 '13 at 0:53
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2Throw out the baby with the bath water is an idiomatic expression that maybe could apply. The whole article would be the "baby," and the erroneous minutia would be the "bath water". Dan: "X is false, so this whole article is garbage!" Stan: "Not so fast, Dan; don't throw out the baby with the bath water." – J.R. Aug 3 '13 at 1:21
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2The Roman legal doctrine was falsus in unum, falsus in omnibus - "False in one thing, false in everything", that is, a witness' falsehood in one particular discredits their entire testimony. It is however generally taken to require intentional falsehood to be applicable. – StoneyB Aug 3 '13 at 1:30
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1The person who claims to have disproved the whole through finding a minor flaw is nitpicking. – Fortiter Aug 3 '13 at 2:56
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I believe this would constitute a special case of the "fallacy fallacy", where an argument or part of an argument is shown to be false or poorly constructed, and therefore the conclusion is presumed to be false as well. I can't think of any more specific term for when the disproved part of the argument is unimportant to the main point.
EDIT: Fortiter's nitpicking fits the bill for this more specific case.
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If there is no established term, I would suggest diversion by synecdoche
diversion: A maneuver that draws the attention of an opponent away from a planned point of action, especially as part of military strategy.
synecdoche: a figure of speech in which a part is made to represent the whole or vice versa, as in England lost by six wickets (meaning ‘ the English cricket team’).
