He says there has been un-handled moisture damage in the bathroom and the kitchen countertop needs to replaced, I know it true ( showed up in the property inspection) . 

My local PHA uses the following list to prep landlords for the general expectation of the inspection: Windows and Doors The windows must not be damaged or missingAll ground floor windows must have locksAll doors leading outside must have locks and deadboltsFlooring, Ceilings and Walls The flooring, walls and ceilings must not have any serious defects such as serious bulging, sagging, large cracks, loose surface or other major damagesThe flooring must not have any serious damages and cracks that will cause someone to trip and fall (peeling/lifting linoleum is often what flunks on this point)The ceiling and roof must not leak.

Problems or issues (damage) they find documents what they will not be responsible for when moving out.

We have found this will motivate even formerly sloppy tenants to make the property shine and precludes any "stick-it-to-the-a$$hole" damage on the way out. ... what's that old adage about flies, vinegar, and honey?

Quarterly is best to avert major damage.

The other component is you might not have time to work on it or want liability if you do not fix it correctly and something happens to cause damage to the tenants items.

I have a clause in my lease that states that negligence on the part of the tenant that causes damage to an appliance (or the toilet/sink/shower), is their responsibility.

Tenant damage=tenant pays. 

How often are you performing inspections of your units to ensure nothing is damaged, no leaks, etc..

You just say it is a maintenance inspection which you are looking for items to fix but real reason is to assess damage they just do not need to know that.You need to know eviction timelines for your state in months and also need to know how much reserves you have if you had to get them out.