Need advice - have you ever evicted for "disturbing the peace"?

My manager wants to evict residents on the grounds that we just gave them their third notice for lease violations - noise complaints, disturbing peace, trash in yard.

My concern is that I have no police calls and no statements from neighbors backing up the violations. They have a late payment history, but it looks like they eventually pay rent and late fees. 

I have no doubt these folks are trashy, but no proof that the lease was violated. I don't want to initiate a Legal Aid nightmare. What would you do?