There is no hard and fast answer. The purpose of the inspection is to make sure there is no damage that needs to be repaired (and/or which has been caused by the tenant); that the tenant is keeping the place at least relatively hygenic; that the tenant has not made illegal, improper, or unapproved modifications; and also, if there is any restriction on occupancy, that there's not too many people living there. So the landlord should be allowed to move furniture, for example, in order to see the wall behind it--that's checking on the apartment's physical condition. He should not be able to open dressers and look inside them, since it's not the landlord's concern what kind of underwear the tenant wears. So in evaluating what may be persmissible, you need to bear in mind the purpose of the inspection, and if it furthers legitimate purposes, it's probably permissible.