That property has central air that doesn't work and I'm going to change out the unit but only between tenants since the current one has a boyfriend that smokes in the unit.

I tell people over the phone that I don't charge an application fee, but that I do prescreen (evictions, criminal background, income, number of occupants, smoking, pets) over the phone before I will show it. 

I have inherited a tenant that has cancer, smokes and has pets.

Smokes and CO on some apartments at turnover, if they are missing they are definitely billed to the tenant.

If your unit fails the inspection for reasons that are nontrivial,  you can then stop the process,  but if its something minor/stupid like needing to add additional smoke detectors in a bedroom and you don't do it you could be exposing yourself.   

(We need to do a safety inspection regarding the kitchen fire extinguisher and the smoke and c/o alarms).Take photos during the inspections, and ask and check about leaks, outlets, and switches.

Apps can't smell smoke on an applicant who also brings a bunch of rude friends with a pit bull in the back seat of the filthy car they drove up in, who was also late to the appointment and you got to admit he's been sleeping on his aunt's couch for the last year after getting out of prison - because you got him comfortable after chatting him up. 

@Kristyn GrimesLol removing smoke detectors from kitchen.

But, additionally, why don't people complain about the smoke and mirrors? 

Take some pics and have some showing the condition prior to move in.When the smoke clears and the adjuster is gone get it cleaned up and rented.