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.
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.
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’).