In my opinion, the most common sources of misinterpretation are these:
The word localized itself has a geographic connotation to many people. Even the Oxford Dictionary defines localize as restrict (something) to a particular place (link).
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it is only relevant to a small geographic area
only makes 1. worse. Also, what area should be considered small?
For example, questions in foreign languages tend to get closed as too localized. If the question is in Chinese, is it really? (I agree the question should get closed, but not as too localized.)
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a specific moment in time
Moment is highly subjective, but I think that most people would interpret moment as something between a split second and a couple of minutes.
I'm not sure myself what is meant here. Is a question that will become useless in 30 days still OK? (The close reason shouldn't be that specific, but I think the FAQ could.)
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an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet.
The last part of the sentence (not generally applicable to the worldwide audience of the internet) is quite unclear. Reducing it ad absurdum, every question that deals only with problem specific to the c programming langage is completely useless for the billions of people that don't know C.
Combining the above with Shog9's comments on the old FAQ, I propose the following change:
##closed as unproductive
Questions and answers should be likely to help future visitors that search for solutions to their own problems. In contrast, this question will only be useful to a small number of people or for a short period of time. See the FAQ for guidance on how to improve it.