However, the odor can be glaringly present to non-smokers.

We realize that many families like / desire pets however, all pets do impose a significant amount of wear / tear / and sometimes permanent damage and odors to our properties that can be difficult / costly to remediate Pet/Animal policy: 1.There will be a $400 non-refundable yearly fee for up to 2(two) small pets (e.g., the yearly Pet fee is $400 for either 1 or 2 small pets).

Odoban on the floor removed some of the odor.  

After the first month, we grumbled about the increased grocery bill, so he sent me $300 via PayPal with a note saying 'January rent'.

Don't want to eat the cost of the floor...don't want my new tenants to smell the odor...don't want to get sued.

Smoke can easily get to those areas that can hold odors.

Do they smell of cigarettes/weed, diesel fuel, body odor?

I guess I'm referring to dog nail marks on a wood floor, lingering odor etc (some dogs just have a musky smell). 

My lease states (removed the parts not at all applicable):Deductions:(a) damages to the Property, excluding normal wear and tear, and all reasonable costs associated to repair the Property;(b) costs for which Tenant is responsible to clean, deodorize, exterminate, and maintain the Property;(f) unpaid pet charges;(q) cost to restore walls, flooring, landscaping or any alteration to the Property not approved in writing by Landlord; and(r) damages to the Property caused by smoking, including but not limited to stains, burns, odors, and removal of debris.Here's a photo of one of the door frames, for example.

There may be issues with noise and odors.