version:JIRA v7.1.9
Situation#1
When clicking on the Watchers' count icon to add a new watcher,it can't search and will say user is is invalid.
Workaround
use the More > Watchers link. it will always work successfully
Situation #2
Strangely,If i use More -watchers to add a people . then remove it and click back to issue. then i can add the user using Add Watchers popup. but when I reenter the issue, The problem has happened again.

As we use a shared environment, so we didn't have global permission.
refer to this link: https://confluence.atlassian.com/jira064/watching-and-voting-on-an-issue-720416442.html
your JIRA administrator must have granted you the Browse Users Global Permission. If you do not have this permission, however, you can still add users by specifying their usernames in either:
- The Add Watchers popup or
- The Add Watchers field on the Watchers page.