When a user starts or ends monitoring an issue, the "last modified" date of the issue is updated and it is brought to the top of the "recently modified" bug list. Personally I think that monitoring does not really change anything about the issue itself. In particular, the monitoring might just be done by a person who is not involved with fixing the issue. Depending on the access rights, a user cannot even see in the changelog if someone else changed their monitoring state of an issue, meaning that to them, the issue looks like it has been updated just a minute ago but they cannot see what was updated.
I propose to not update the "last modified" state when a user starts or ends monitoring an issue.