There are the obvious conflicting traits like Active & Lazy, Friendly & Aggressive, etc., but Smart ('Clever' for cats) actually has some hidden conflicting traits that I was able to track down and remove from pets so that I could assign them Smart. Not all of the traits can be assigned to just any cat or dog.
:D The changes need to be made to one of the same resources that chingyu1023's mod for sims uses, so I will talk to him/her about that.