It's not necessarily correctness for its own sake. Sometimes it's the linguistic equivalent to pointing out a spot of mustard on someone's shirt, which is a courtesy in my book.

That being said, an audience member pointing this out to someone on stage is a net negative. But I'm not convinced that I should ignore irrelevant errors altogether, especially for errors that people use as signal levels of education or intelligence (nuclear and nucular, you're and your, etc.).