I work at a shelter and we treat any of the above mentioned problems for people after they adopt. We have a low cost spay/neuter program on Wednesday so we have a vet on hand that day and request that people bring their new pet in then so we can get them checked. We also tell people that adopt cats to expect a possible URI from the stress of the move and to call us if that happens. We provide the medications if they get sick.
We do our best to clean ears and treat for mites before they leave but sometimes things are too crazy and it gets overlooked. We also have the free insurance for 30 days after an adoption too.
We feel like anything that happens in the first couple of weeks should be taken care of by us. Like it was said before...if they were still in the shelter we would have to do it anyway.