@Lisa Casey
I have not read all the comments, but I scanned through the email quickly.
This is another reason why I only do TAW. You should check your landlord/tenant rule. In MA, there is no grace period, when tenants don't pay on the day it is due, a 14-day notice can be sent out the next day (if you choose to). This can only allow to occur 2/year. The third time, a rent is not paid on the due date, you can trigger an eviction immediately.
Your unit looks good from the pictures. Talk to the tenant that the unit was shown at the time as is, and no written agreement that anything will be addressed upon move in, unless new obvious failure occurred like heat/plumbing issue ... etc. I think without proper inspection, it is not easy to determine that if the unit is inhabitable. To properly determine that, a board of health will be involved, in which you should not anticipate.
You can counter offer a new proposal in person that anything discrete like fixing hole in the ceiling will be fixed (you have to fix it anyway even with a new tenant ..), and anything else "is as". They may choose to break the lease and move on if they don't like. Tell them that if you make the fix (minimal), payment will be due exactly on the due date.
The tenants don't sound like a professional. They just want to prove that they are aware of the law, they are going to use it, and that is their leverage to the discount negotiation.
They are looking to negotiate and work with you. Clearly there are minor cosmetic problems that they think you should look into. They sound frugal or financially distress as they think about heat and air conditioning performance.
Knowing that the husband does not have a job for so long, they are trying to renegotiate for 30% discount. Another option is, you can accept the 30% discount and ride it out until the end of the lease with an addendum of all acceptable as-is condition until the end of the lease. At the end, you should not renew the lease.
In general, I don't want to keep any tenant that is too intelligent and understand rules that can put fear on landlord ... etc. I think by presenting them with an eviction after the email is considered retaliation. At this point, if it is going to hit the court, I would hire an attorney.
This is not any legal advise. It is a perception ...