I've heard various ideas such as limiting it only after mods have expended their points (this will require implementing a cooldown to prevent a user from getting points again too soon). I want to hear your feedback, and I'll roll together something for the next major update of the site. Leave your comments
dive right in and use up their points straight away
That advice may be misinterpreted by some people. For instance, I sometimes have mod points and open up a story, and read all the comments... and then don't make a single moderation. This is because I'm trying to avoid the 'early mod-up' effect. For instance, the first comments to a story may not end up being anywhere near the best comments once more time has passed. But moderators may feel the impulse to mod-up the best comment posted so far, even if it's not particularly insightful or useful. This leads to highly-rated comments that are lacklustre. (They are not necessarily bad, but perhaps not the best.)
In other words, I think the criteria for up-moderation should be 'this comment is genuinely good/useful', and not merely 'this is the best comment I've seen so far'. If a given comment thread ends up having no highly-rated comments, that's not necessarily wrong (maybe there were no worthy comments).
Modding in the way I suggest does mean that mod-points sometimes expire without being used. And it does mean that there are fewer highly-rated comments. But in principle it means that the visible comments are of higher quality. So I think it's worth it.
I agree with when you say "open up more stories to finish my duty of using up those mod points"... I think the general moderation task should be of the form: "Keep going back through stories until you find worthy comments". I.e.: don't just moderate the first few stories (that have few comments and few moderations), but instead keep going back in the post history looking for worthy comments until you run out of modpoints.
Yes, I think we are broadly in agreement about the approach to moderation, and that the wording I chose might be misinterpreted.