Captious, nit-picky behavior in a professional context usually signals to me that there is another problem that is worth attending to. e.g. A person raising a series of petty objections in a meeting may have deeper problems with the plan that she can't yet articulate, or is being put in a position of apparent but not real authority (that is, "the ship has sailed" on a decision without real agreement being reached).

Telling someone to more or less shut up might pay off in the short term, as in make a particular meeting go faster, but in the long haul you're ignoring a pretty telling symptom.