It would be really helpful if users had access to more "p4 monitor" functionality, at least for their own processes. For instance, if a user could run "p4 monitor show -l" against their own processes, it could help them track down long running processes or other problems. Knowing what they submitted rather than simply that it was a submit might clue them in on which system or window the problem is in, for instance. (We have engineers with dozens of terminal windows open, sometimes across several systems).
If necessary, add a "-u <username" option for the options with this extended functionality, and make sure it matches the invoking user. That would actually be helpful for admins as well.
It's worth considering allowing users to run "p4 monitor terminate" against their own processes as well.