I had this issue in my current role and devised a separation of duties for the mailbox monitoring. I work 2nd shift, with 2 other individuals (one who isn't full-time) and the companies SOP is that the service desk inbox is monitored 24/7 to keep or SLA's. Well, the issue that you brought up was a problem as any 1 of us could inadvertently click on an email and it would go into read status, causing problems if the email needed actions taken. I divided the mailbox duties between myself and the other full-timer so that the first half of the shift is my responsibility for the inbox, afterwards would be the other persons.
**If one of us had clicked on an email and it was not already in read status, then we all agree to place the Unread status back on that email for the person responsible to deal with.
Hopefully this helps as the only other way I know to deal with this was address by AndyDavid.