I have changed the sharing rules on various records and the role structure for my organisation, but now users are unable to edit cases, change status or owner; or email from the case.

The error message that users see on the screen is:
Error: Invalid Data.
Review all error messages below to correct your data.
Apex trigger ShareUserPermission caused an unexpected exception, contact your administrator: ShareUserPermission: execution of AfterUpdate caused by: System.SObjectException: Field is not writeable: CaseShare.CaseAccessLevel: Trigger.ShareUserPermission: line 16, column 1

I also receive an email as below:
**
Apex script unhandled trigger exception by user/organization: 005900000010qIR/00D90000000iHod
ShareUserPermission: execution of AfterInsert
caused by: System.SObjectException: Field is not writeable: CaseShare.CaseAccessLevel
Trigger.ShareUserPermission: line 16, column 1
**

I think the issue is similar to this:
https://help.salesforce.com/apex/HTViewSolution?id=000149002&language=en_US

But I have no idea how to resolve it. Help!