It needs a new carpet, the owner offered to put new carpet or give a carpet allowance.  

I would tell them they need to return the property in the same condition. any cost to you that isn't already necessary will come out of their deposit. for instance if the carpet was old when they moved in you probably can't charge them to replace it but if it was new and you need professionals to come in and clean a stain out from s glass of wine, I would charge that

Carpet, paint, switch plates, blinds, etc.

Unless you are doing the work yourself, a new furnace will cost $3,000 and the flooring will be about $800 if you use carpeting.  

Reminds them about end of lease procedures as well, notice, carpet cleaning, etc.This gives them a 1-page reference because as @Casey Miles mentions they don't read the lease after we have gone through it on signing day.

The other unit is vacant and was recently updated with new carpet, cabinets and laminate kitchen countertops.  

No rent for three months plus fees, cockroaches, and ruined carpet, beat up walls, etc.Today, her sister called me to tell me she had passed.

We’ve done some minor cosmetic improvements like changing carpets to laminate.

It is recently remodeled house including a new deck, tiling, carpet, and a mud-room addition.

If yes then I think all I need is to replace carpets with laminated flooring, repaint the whole unit, replace all appliances, repaint the kitchen cabinets.