From a pure investment standpoint I know it's lower than what the market would demand.  A

That's why banks demand a personal guarantee when you borrow.

Can a tenant demand a new appliance if fixing it becomes ridiculous?

I was cash poor and the house's demand as 1 of 3-4 like it in the whole 'hood meant vacancy risk was mitigated.How did you find this deal and how did you negotiate it?

I would definitely tell the manager that you straighten this out with about the confusion and demand a discount.

That should give you a sense for demand as well as satisfaction of the renters in staying in that area. 

When, or if, they demand a reason you simply inform them you do not specify reasons and then hang up the phone.As a landlord you are not, in most jurisdictions, obligated to justify your decision to applicants.A rejected applicant can not take action against a landlord unless the landlord is stupid enough to verbalise their decision to reject based on identified protected classifications.

How can they demand a return when you have no place to send it?

I have a few co-workers who have moved to the area and these properties seem to be in high demand as rentals with lots of new construction in the area. 

Let the tenant/mouse have a cookie and they'll demand a glass of milk.I agree with what others have said about the repair issue.