I've been noticing for some time that some of my stories are reported as having 0 comments, and some have the field for number of comments blank.
(And then, some report a positive number of comments.)
Now, it would be easy to understand having the field blank; it would be easy to understand reporting a zero. I cannnot understand why some have one and some have the other.
If the story comments facility is not turned on for the story that field will show blank, if it's turned on and has no comments it will show a zero, if it's turned on and has comments it will have the number of comments lodged.
The story comment is a fairly recent addition so older stories may not have it turned on. I'm not sure if the current default is on or off.
edit to add: If you go to Authors / Editors >> Story Stats >> select the story concerned you'll then have a page about the story with several boxes at the top. The left hand box in the third row will read either 'Hide Public Comments' or 'Show Public Comments' - whichever is the opposite of the current setting. Thus clicking on the box will switch the setting to what it says.
Also, if you go Authors / Editors >> Manage Stories >> there's a box near the top of the page where you can turn the story comments on or off for all of your stories in one action.