Clean configuration cache across the farm
Sometimes cleaning the SharePoint configuration cache is required. This is a rather simple endeavour:
List ActiveDirectoryGroups for a user, using PowerShell
If one needs to know the AD Groups a given user is a member of, there are several ways. Some of them are described in an old TechNet article. Another method that is very easily used in PowerShell is ADSI mainly because it is part of every PowerShell and no aditional installation is needed.
Sync BackConnectionHostNames across the farm
Sometimes a customer does not have a GPO in place for setting BackConnectionHostNames.
In these cases one has to manually connect to each server in the farm, open RegEdit and set the values accordingly,
every time a dns name of the farm changes.