If the previous smoker was a heavy indoor smoker (probably the case in light of the lingering smell) then the odor can penetrate sheetrock more than most people realize. 

So they are basically paying for their gas cook stove while I am still paying for heat.  

@Deanna McCormickThey weren't smokers.

I would send them notice of three violations. 1) lease says no pets...get rid of the cat before it destroys the property.2) stop smoking on the property or face eviction, offer to release any smokers from the lease.3) cure the insect infestation immediately.Inform them you will me making regular inspection visits and expect the issue to be resolved.Your other option, if you have no desire to inforce your lease is to tear it up and write a new one that you do intend to inforce.

$400.00 Bucks, Please tell me this new Vista is going to be able to cook, clean and wash the car at least three times a week.

Maybe the tenant isn't as good of a cook as he thinks he is.

I wasn’t so convinced.So my next call was to my main teacher and mentor Bill Cook.

If you're going to eat you need to cook your meal which means you need to stand close enough to the stove by the fire.

I'll be there. count me in on whatever you cook up. if I can do anything let me know

@Angie Cook Timely post!