Reasonable delays in repairing are okay, though in certain circumstances, they can withhold a few days rent.

The tenant can call fair housing and withhold rent based on the property not being safe-mice carry germs.

The kind of tenant who 1. allows another to occupy without permission, 2. is dishonest (or at least withholding) about his occupancy, and 3. allows him to smoke inside - probably not the best in the long-term.

If you tried to withhold the deposit the tenant may decide to press their case in course and you would most likely have a difficult time convincing a judge that these issues are the tenants responsibility... especially since you don't have evidence of the condition before move in.Anytime I am purchasing a property where I am inheriting tenants I always assume that I will be returning the entire deposit to the tenant and I build that into my numbers.

And then she says she is now withholding rent because of 'mold', but she stays there.  

Back then I can have a cheapo painter do a 2BR apartment for $500, so for $200 more, I can have the whole apartment painted, spackling holes included.But the worst part is some tenant gets so mad at you for withholding part of the deposit, sues you as a matter of principal, and you have to go to court.

If she asks for an outside hose bib, do NOT do so, unless it's in the lease that you will provide this.If she threatens to withhold rent because you haven't done what she is demanding, don't respond. 

Tenants usually have the legal right to withhold rent for the time they dont have essential services.     

If the landlord fails to send you a list of damages, they forfeit the right to withhold the security deposit.The security deposit, plus interest, less any damages rightfully withheld, must be returned within 45 days of your notice."

If you are renting it out and it's a low priority you can probably get away with holding off on doing it until you want to spend the money to do it.