When is it okay?

If you know someone is causing a problem.. bad mouthing people, inappropriate suggestions or comments, seriously bad manners...

When is it okay to confront them, and how?

Keep in mind that we don't want to embarrass this person (regardless of what they are say), and we don't want others to know that we are talking to them (to correct them).

I think it is ok to confront them right away. but it depends on the situation. Is this someone at work? Someone in the family? A neighbor?
I would start off by calmly expressing how you feel about their behavior and see where it goes from there. Since I don;t know what relation this person has to you ( family, co-worker, etc) it's hard to give much advice about how to go about it

Semi-transient Congregant.

Then I would do it as soon as you can. In private if possible so as not to embarrass the person and put it as gently as possible. If it works, great, if not, I would be firmer.