It depends on the context. A lot of people have been poorly taught, and they repeat mistakes from their school or family. Some people are nasty correction police, and they correct everything even if it's an "acceptable" regional difference.
If it holds them back in their job (which it does often), it can be helpful to gently suggest that others form an opinion about your intelligence or level of education based on common mistakes such as saying "nucular" for "nuclear" or grammatical errors like "My co-worker was annoyed when the boss reprimanded her and I." And if the individual's job requires writing correspondence, reports or newsletters, or doing any kind of public speaking (from answering phones to giving tours or sales pitches), then poor grammar is a huge problem that gets in the way of advancement.
Some people just try to model the correct pronunciation and hope the person gets the hint. I remember seeing a movie years ago that dealt with "Celtic folklore" and I was telling someone about it . I pronounced "Celtic" with an "S" sound (as in "Boston Celtics"). The person just listened and then responded in normal conversation, but pronounced it like "Keltic" - I heard the difference, looked it up on my own, and never made that mistake again. But I had a good education, had teachers who corrected my spelling and grammar, learned to use a thesaurus, and (an important factor) learned a second language. Learning about another languages grammar and the parts of speech (direct object pronouns and the subjunctive tense, no less!) helped me do a much better job with English.
It depends on how the corrected person views the correction: is the "corrector" trying to make me feel small and inadequate, or is this helpful to my advancement and my being seen as an intelligent person worth listening to? If my mistakes make the listener feel that I am careless in other ways, or that I don't care about my finished product (whether it's my work or my conversation), then my poor grammar reflects badly on me in a way I want to change.
In the case you cite, the correction was done privately, which is good. If it was done by a boss or a friend, then your pal should see if she can learn from it. If it was done by a store clerk she'll never see again, then the context was probably inappropriate. It also depends on HOW it was done. Sometimes saying, "I've always wondered about that word. Some people say X and some say Y. I'm going to look that up so I get it right" is more palatable than "YOU screwed it up and I am always right about these things."