"Even acknowledging the Compelling interest that the city has and societal benefit, it could not override the landlords' fourth amendment rights"
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I'm not sure that landlords have fourth amendment rights in premises that have been leased. The entire point of a lease is that the landlord is ceding control and possession of his property to another. That raises a standing issue; the fact that I violate your rights (tenant) does not give a third party (landlord) standing to sue. Unleased? Sure, I agree landlords do have a right against unannounced inspections.
Here, however, we have the actions of the tenant creating liability on the part of he landlord in situations where the landlord might not be able to control/over rule the tenant; as one poster here said, how many landlords have government co-operation clauses written into their leases?
As written, I think the inspection ordinance goes to far. As I suggsted it be written, however, inspections are jake.