Use comments to point out problems, but take longer discussions to chat, and always remember to Be Nice.
In my view, the best workflow would be like so:
- The OP posts something with factual inaccuracies
- Another user points out the flaw in comments, explaining the issue clearly and, if possible, suggests a way to fix the error
- The OP edits to fix the problem or, if the post is unsalvageably wrong, deletes their post
- If the post was edited, the OP should then flag the comment as 'no longer needed'.
A wonderful piece of advice I read was this:
Criticism is futile because it puts a person on the defensive and usually makes them strive to justify themselves. [...] There is only one way under high heaven to get anybody to do anything. Did you ever stop to think of that? Yes, just one way. And that is by making the other person want to do it.
— How to Win Friends and Influence People, by Dale Carnegie
Once you reach the stage of arguing, you'll never get anywhere with actually fixing the problem. And fundamentally, fixing the problem is what you want when you leave critique—or at least it's what I hope for when I do. So I try my best to be constructive when commenting, because I want to help improve posts, rather than get into heated debates with others.
But sometimes, no matter what you say, you can't agree with everyone else. Your viewpoint might be completely different on a solution to a problem. If you're in that situation, it might make more sense just to drop it rather than fruitlessly argue on and on.
Nevertheless, it is still helpful to leave a comment explaining clearly why an answer is not correct—as well as being mentoring for the OP, comments can act as 'signposts' for anyone else reading the post—a friendly 'watch out' to stop people going down the wrong route.
I realise I've gone on a tangent here, but I hope that gives you something fundamental to think about before I get to the real points:
I recommend pointing out issues with answers and suggesting improvements in comments. Since they're directly below the post, it's probably helpful to write your critique there so that other readers see the potential pitfalls with an answer.
If the OP doesn't agree and wants to discuss the point further, it might be more productive to get a chat room and leave a comment pointing to that room.
But remember that the Be Nice policy always applies, in comments and chat. If you see a comment chain going the wrong way, please let us know. You can flag particularly concerning comments directly, but if you ever feel uncomfortable with the direction of the comments on a post (e.g. if it's more a case of getting the last word in than actually discussing a point), feel free to use a custom flag on the post itself. Don't feel like comments have to be blatantly offensive before you can flag; if you feel like the 'Be Nice' policy isn't being followed, or the comments aren't getting anywhere, feel free to flag.