"Comments are not for extended discussion" is in my opinion a very valuable thing to imbue in the community.

Occasionally I've been on one end or another of the following situation:

• Person A makes a comment / statement
• Person B leaves a comment / feedback
• Person A resolves the issue and wants to say "thanks" or "done", etc... but refrains
• Person B now has a hanging comment that should be removed, but they don't get notified that action has been taken

For example:

• I recently commented on this question, with an initial "please note that shopping recommendations are off topic", followed by a brief answer in a single comment. I was in two minds about including the off topic note, but did so anyway.
• grawity then (very fairly) pointed out that the OP did indeed ask in a compatible way.
• At this point, I wanted to say something along the lines of "thank you for pointing that out, I've removed my comment and written a more complete answer", notifying grawity, and allowing them to remove their comment. In fact, I did that, but then deleted it ~10 minutes later... (indecisive much?)

Another common example is a request for more information... e.g: "Please share the output of x". Once the OP has provided the information, the comment is often stale and unnecessary - people typically comment again saying "done", or rely on responders coming back to the question to see if there is an update.

So... what is the most suitable resolution here?

• It's not an issue that needs to be addressed.
• Introduce a new feature such that authors and tagged users can acknowledge a comment, notifying the commenting user.
• Person A responds with such a comment anyway, Person B is notified and deletes their comment, but then Person A has a hanging comment...
• Using flags as suggested by Journeyman Geek below is suitable, despite the fact that users don't get notifications.