We have assigned the Wordpress Access Control permission “CiviCase: access my cases and activities” to a variety of users who we want to assign case roles to. The description of “CiviCase: access my cases and activities” permission indicates that users with this permission should be able to view and edit case activities with cases they are associated with.
Users with this permission can view the cases that they've been assigned to, but they are unable to edit case activities and add case activities on cases that they’ve been assigned a role to. A popup box that says "Sorry, an error occured. You are not authorized to view this page" appears. The only way users assigned to a case are able to edit and add new activities to a case they've been assigned to is to enable the permission "CiviCase: access all cases and activities", which is something we prefer to not enable.
There are at least two threads in CiviCRM Stack Exchange about this issue. It's a significant issue for organizations that will rely on Civicase.