I think there are two separate issues here.

If you think you found an error in a paper, you should never discuss it on a public forum before giving the author a chance to think about and correct it first, in my opinion. Of course, it is sometimes difficult to tell whether a point which you have realized is an error in a paper or not, but if you think that there is a good chance that it is an error, it means that there is a good chance that your post on a public forum might embarrass the author of the paper, which is probably a situation you want to avoid. Although all of this is pretty general, a sentence of two on this point in FAQ on cstheory.stackexchange.com may be useful.

(Therefore, as a tangential topic, I have some uneasy feeling about the discussions on the recent paper by Vinay Deolalikar. I have never followed the discussions closely enough to draw any reliable conclusion, though.)

However, a question or a discussion may reveal an error of a paper in an unexpected way. In that case, it would be better that someone contact the author to let him/her know about the finding. I do not think that moderators are the most suitable for this job, but if someone not in the discussion notices a case like that and it does not seem that anyone has contacted the author, it is probably good to draw the attention of the moderators (by flagging the post) and ask the moderators to handle the issue than to contact the author directly. To make this work, if someone (in the discussion) contacts the author, it is a good idea for him/her to drop a line in the forum so that other people do not have to worry about the possibility that the author might not be notified of the discussion.

I think there are two separate issues here.

If you think you found an error in a paper, you should never discuss it on a public forum before giving the author a chance to think about and correct it first, in my opinion. Of course, it is sometimes difficult to tell whether a point which you have realized is an error in a paper or not, but if you think that there is a good chance that it is an error, it means that there is a good chance that your post on a public forum might embarrass the author of the paper, which is probably a situation you want to avoid. Although this is not specific to this particular website, a sentence or two on this point in FAQ on cstheory.stackexchange.com may be useful.

(Therefore, as a tangential topic, I have some uneasy feeling about the discussions on the recent paper by Vinay Deolalikar. I have never followed the discussions closely enough to draw any reliable conclusion, though.)

However, a question or a discussion may reveal an error of a paper in an unexpected way. In that case, it would be better that someone contact the author to let him/her know about the finding. I do not think that moderators are the most suitable for this job, but if someone not in the discussion notices a case like that and it does not seem that anyone has contacted the author, it is probably good to draw the attention of the moderators (by flagging the post) and ask the moderators to handle the issue than to contact the author directly. To make this work, if someone (in the discussion) contacts the author, it is a good idea for him/her to drop a line in the forum so that other people do not have to worry about the possibility that the author might not be notified of the discussion.