On the JS Menu notifier, it shows I have 6 unread messages.
However, on clicking the icon, the pop up shows that there are no unread messages.
(The problem arose after some testing that we did with integrating another component, so its not a JS error per se)

How (or where) do I manually clear this for this one specific user (I have access to all files and database records)

Hi Marc,

It can be database problem, containing "dirty" records maybe.
for unread message counter at notification, jomsocial using countUnRead function at /components/com_community/models/inbox.php
on that function jomsocial always count it by using query at inbox table. so there is no "counter number" that stored at database.

could you please provide me FTP and phpmyadmin/cpanel access detail? I need it for debugging purpose.

Regards,
Albert

Thats perfect. Just needed to be sure which DB table was being used.
In this case the message was deleted but will still marked as unread and not deleted.
Simply ticking the messages as deleted solved the problem.