Here is the law on evictions:http://www.dca.ca.gov/publications/landlordbook/te...Normally, yes, you could give them a 3 day notice to comply with the lease or quit.But.These guys have put the screws to you, maybe knowingly and maybe not, by asserting a right.  

Now that I went to the trouble of identifying mold testing/remediation resources my tenant -- who asserted that she is living with toxic mold -- has not reached out to those outfits. 

I will take Penny's suggestions to type up the criteria and assert that along with applications.

He also asserts that I am unethical as I “aggressively seek out tenants with loud barking dogs” (perhaps 2 of my 5 tenants in a dozen years have had barking dogs).

I'm assuming OR is the same, because of what was said, but in CA you can't kick out a tenant for 6 months after they assert a right, or it's considered a retaliatory eviction.And she probably knows this.Which is why I'd not let her just get away with throwing a piece of paper on the desk and refuse to comply with a process that is legal and reasonable.  

your assertion is that sigarette burns damaged the carpet but you cannot prove was caused by the current tenants.  

There are some in here who will assert incorrectly that it's their house and they should be able to select anyone they want.  

I disagree with your assertion that you "know your neighbor."

I am sitting at my office and a guy comes storming in with purpose, decked in full suit, sunglasses still on, very assertive.

Get the survey done and if the land is yours, assert your claim through your attorney.