Objects are used across all policies in a single Smartcenter. So when you need to change an object it will apply those changes to all policies it is used in.
When you are looking at a Multi Domain environment you can use global objects, which you can use in each policy that you apply that Global policy to, even if you only put a any any drop (cleanup) rule in it, you can choose to apply all objects to each Domain you assign the Global policy to. So then, when you change an object in the global policy, you reassign the policy and then you could even push policy to the gateways of each assigned policy.
Keep in mind that changing a Host or any other Network object it will NOT show that the Global policy has been updated!
Regards, Maarten