If I published a mistake, then I would be grateful to hear about it. Firstly it shows that someone has actually read my work. Far worse would be to discover your own mistake years later and realise that either nobody read it or nobody cared enough to correct it.

Of course you may be mistaken that there is a mistake, so you shouldn't just say flat out: "there's a mistake", but rather "I believe there's a mistake, and here's what I think it should be. What do you think?"

What Now? Discuss the "what now" with the person involved. If you both agree with what should happen then great. If you disagree about there being a mistake then talk privately with others to see if they agree with you or not. If all else fails then publish the corrections yourself if you think it is worthwhile to do so, but firstly tell the person that you are going to publish, as that gives them one last oppotunity to do it themselves.