Roof, furnace, and A/C are all in good condition and reported to be functional.

May not work, but always worth asking them to get it taken care of, some liability issue potential there. 

First of all, do not rent to tenants who don't take care of your property (bad "hygiene hobbits") and allow an environment/condition in which pests would take over.  

If he gets it done by the end of the month, we return his full deposit and we'll take care of whatever junk he doesn't want.

Does that really take care of the mold that attached to the flooring (due to the moisture issue after the mold crept up all the walls it flung itself onto every single thing in that house lol including the floors), or is it like mold on bread where the mold has roots and is all over inside even when the surface is sanded off?

See, on those days, and they will happen, you'll pull out your handy Rolodex and look up the contractors (and lawyer) you have relationships with and get those jobs taken care of lickety split at a good price because you're a local with repeat business.

Nevertheless- If you've taken care of the bldg the way I know you have then the building violation & your case against the tenant will travel along different tracks.  

Care to share the financial details?  

Short term (1-2 years): generate $2,000 cash flow after expenses per month (child care costs)2.

The guy wants to sell because he is a doctor and does not have the time to take care of the property.