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My opinion is that it should be completely acceptable. Of course, a very specific question might be interesting to only a very few people, in which case it's not likely to attract more than a few votes. But I wouldn't take that as a sign that it's not acceptable.
If it is well motivated and enough background/reference is given, and if the paper is of research level, then such a question should be acceptable. If it looks like a homework question in disguise without motivation, there will be objections.
I think a good example looks like the following: "I am researching X using the paper Y, where on page 6 the author says Z. I am surprised because I thought Z' was true, and it seems that the context (specifically the assumption of W), would prohibit Z because (something W implies that is far from Z). Can someone help clear this up for me?"
The example above can be modified to show what work you have done in attempting to resolve your own difficulty, and where you got stuck. You might include pertinent online references that are freely available if the paper itself is not.
Gerhard "Ask Me About System Design" Paseman, 2011.11.15
@vinoth: what Tom said. It can help to bear in mind that voting on MO is sometimes a little weird. You shouldn't worry unless people complain!
+1 Deane. Not all MO users have institutional affiliations, and even those who do might not want to track it down.
I think one of the interesting differences between MathOverflow and StackOverflow is that, on MathOverflow, the most appropriate questions are the ones that don't get very many upvotes, because one of the features of mathematics is that important technical questions are only understood by a few people.
@dan petersen : sometimes the question gets asked because e-mailing the author isn't exactly possible
I also completely agree with Deane. And I put my money where my mouth is (see the above link).
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