Tenant sworn dog was trained and well behaved and on day 2 of the pet's arrival we have damages to the front door and one interior door (as well as some furniture damages but those are not mine).So I am trying to decide how to go about deciding whether to replace an item or repair an item.For example, this is the corner of an interior hollow core door, the entire corner has been chewed out. 

Apt is on ground level (first floor) with ceramic tile floors throughout.Current lease has no pets and no water-bearing furniture clause.

J. beard not hiding at all. or expecting to have that from a pm. the mistakes have been plenty for example manager gave ok to tenant to move larger furniture in 7 days before lease starts. and they slept there, thinking they could 'move in'.

Furnish it with decent furniture from Cost Plus or Pier 1, and furnish glasses and dishes and pot/pans etc, then try for a family who is transferring in or an upscale or corporate type.

For instance, I can't put a certain piece of furniture on a certain wall as it would need a long 4" wedge on one end to even it out).These are the massive issues that are against code (that I know of.)

He wrote me a check for some furniture I was selling at my garage sale, and the check bounced.  

Cats may also have claws that will ruin things (but usually that just tends to be the case with furniture), have hairballs and accidents.  

This is in North Carolina, if it matters.If tenants turned keys over and signed a document stating that they have vacated the property and returned possession to the Landlord, are we under any obligation to keep the possessions (mostly random trash/small pieces of furniture/paintings/food/etc., likely less than $100-200 of value total) for a set period of time, or can we simply dispose/donate as needed?

Picture a bed and furniture in there.  

Your typical big dog is going to bark less and pee on the furniture less but that's more personal observation than fact.