Sorry if I've not been clear enough. I'll try and explain by answering your questions below:
Are you saying you have users who are part of a department group, and each member in the department group has the rights to view and complete tasks assigned to the group? - Yes I have users as part of a department group that can view and actions tasks. I've then setup team groups which only the respective team members are in. All team members within the team group can see all INC/SR/PM and CH requests and all department groups can see all teams INC/SR/PM but not CH requests?
In regards to the tasks, this is different to rights to view Inc, SR, PM's and Changes (all requests), this is handled through roles, and users are assigned roles to govern the request types they can work with, and what rights they have for example, Incident assignee role compared to Incident full access role. - Yep, I understand that rights are handled by roles and all users have the correct roles assigned to them to view/actions INC/SR/PM and CH requests.
There is then the second level of visibility which is about the users only being able to view requests which are logged against services which they support. - Again we have set all teams to have access to all the services and their requests assigned to them.
Are you saying users can't be assigned / view Change Request Tasks? but they can for tasks linked to Inc, Prob, SR's etc? - No, I'm saying until users in the department group can only see INC/SR and PM and not CH requests. If I then add them to the Team group they can see all requests. This makes it whole point of setting up teams a pointless.
There is also the issue of what you can do with tasks which are assigned to other members of a group - There is a also an experimental feature called - advanced request task completer which may help here:
https://wiki.hornbill.com/index.php/Service_Manager_Experimental_Features - This is separate but will definitely help with this issue. Thanks.
This feature allows a user to complete tasks that are assigned to another person. Supporting teams of a service that is associated to a request will be respected otherwise if a request is not associated to a service, then the user can complete tasks that are assigned to the user's team(s) members.
I hope the additional information helps.