Most of this is your fault for not checking and taking care of issues. First of all, I suggest you never have tenants fix or repair. They are not licensed, why would you want them reparing anything? Use a licensed contractor. You should be changing AC filters. It may be the tenant's responsibility to clean mold, but when you inspect and they are not doing so you give them a written notice to clean or you will have a cleaning crew (that deals with mold) clean and charge them. Why are you asking the tenant to paint?
Seems you were aware the dishwasher was old. You should be conducting yearly or even better twice a year inspections. Look for leaks around dishwasher connections, pipes, mold cleanliness and check all appliances/air con-heater units. Preventive maintenance will save you so much $$ in the long run.
Trouble accessing unit? Post a 24-hour notice to inspect/repair and you are entitled to go in. If they deny access, call the police.
They may be lazy and unclean tenants, but you seem aware of this for a lengthy time period and allowed it to continue. Without giving them any type of written warning for these issues, you may have difficulty making them leave if they challenge it.
Since you have some empathy for the woman's plight, I suggest you start by listing all of your concerns/lease violations in a written notice and give them a copy. Make sure they understand the unit must be maintained and all your concerns addressed from this point forward.
Also, require them to report all maintenance needs in writing to you within 24 hours from which they are aware of the problem.
Sorry, but I think a lot of this is due to you being a laxe landlord/owner.