Is it possible to be able to set a ticket as private so that it cannot be seen by another agent (unless perhaps they're a global administrator, in which case a warning is shown before viewing the information)? A few instances where a request or incident may be confidential or sensitive.
That's a good idea. One way around it might be to create an Agent Group called "Private" and change your agent access settings to only allow them to view tickets that are assigned to them or the groups for which they are members.
I would go further and when a Ticket is set to PRIVATE, only administrators or agents involved in the specific ticket (have been assigned in one way or another to it) are able to see it.