Hi Brian,
Of course you can sue your previous tenant for the damages but you have to consider the opportunity costs of your time, money for court costs, stress, etc. After all of that, chances are the court will find in your favor and issue a judgment which you will probably never be able to collect unless your tenant decides to buy his/her own home one day and needs to clean up their credit. Experience has taught me that those that can live in really dirty homes without being bothered aren't concerned about having "clean" credit.
I would just learn as much as possible from the whole experience and make sure that regular interior care obligation walkthroughs are performed on all of your properties in the future.
Check out
this thread. Sounds similar and worth the read.