>1. Does the 'not constructive' flag have a strongly negative connotation within the system?

Yes. [Posts with comments with such flags are flagged again for further review by moderators.][1] 

> If a user’s comments are consistently flagged as rude/abusive or not constructive, a moderator flag is raised. ([source][2])

So it's more important lately to get this right.

>2. If so can we have more detailed clarity on it's use?

I understand Stack Overflow is working on revamping the flag system, but until they do, we have to work with the system we have. 

My direction is to flag as Not Constructive things that are borderline rude, negative, and don't add to the discussion. Follow these steps in order:

1. If a comment is clearly Rude or Offensive, flag it as Rude or Offensive. For (meta)example: 

   > - Your religion and politics stink - Delete your account!
   > - Your mother was a hamster and your father smelt of elderberries.
   > - You should have learned this in kindergarten, you ignorant bumpkin.

2. If a comment is clearly benign, but Too Chatty, flag it as Too Chatty. For example:

   > - Thanks! That answer really helps and clears up things for me!  
   > - You're welcome, please use the answer in good health.
   > - Reminds me of [the time I caught the ferry over to Shelbyville.][3] 

3. If the comment is somewhere in the gray area between rude and benign and adds no value, flag it as Not Constructive. For example:

   > - Use a search engine before asking! 
   > - Don't bother trying to support last year's technology, those users aren't worth it.


4. If a comment is Obsolete, flag it as Obsolete. For example, should be obsolete once they've been actioned.

   > - Can you edit your question to show us the code you're using?
   > - Can you fix a particular problem with your answer?

>3. Can we have some mods' perspectives on this?

Here's my perspective -  
Moderator time is best spent looking at actual problems. When "thank-you" comments cause a post to get greater scrutiny at the expense of posts where people are actually escalating a back and forth, that's a problem.

If I have a private moderation conversation with a user, I don't want to tell them that they have X many Not Constructive comments, only to be challenged and on closer inspection finding them incredibly benign.

Empathizing with new users: if I were a new user who said, "thanks!" a lot, and my comments were being characterized as not-constructive, and it was brought to the attention of others, either by myself or some other leaky communication, I'd feel like the system was treating me unfairly or capriciously.


  [1]: http://meta.stackexchange.com/questions/284053/community-deletion-of-comments-should-raise-a-moderator-flag/284058#284058
  [2]: http://meta.stackexchange.com/questions/252844/make-comment-flags-less-stupid
  [3]: https://www.youtube.com/watch?v=-o-7MmhqNfA