While your apartment may allow pets, you should check with your landlord if you are mid-lease what will be necessary from you to have a pet. Usually there is a large pet deposit required. You just can't have a dog without specific permission.
As far as what the inspector will be considering will be things like if you have dangerous stuff or food the dog could easily access or if there is ample space to exercise the dog available. They may also require you to have a crate. You don't need to be **** and span but should be tidy.
If you have a spotless house and you want to foster a dog, someone is going to think you are nuts. Don't worry about it, just pick the place up and clean a little.
I think the cleanliness of the apt and safety of the dog are the top priorities. Just have a clean home in general. If you have a patio it should be clean as well. If you don't have any pets that would be a plus so they know there won't be any conflicts with socializing two animals.
Just make sure there isn't anything bad the dog can access, maybe put a locking mechanism on the cabinet with cleaning supplies...that's about it. As long as your place is tidy and clean, you should be just fine.
I want to foster a dog, my apartment allows pets and I applied to be a foster parent at the adoption agency. They will be inspecting my apartment and suite what to expect and what do I have to look like and what do I have clean to be approved???