1. I'm not convinced Shinzon was truly insane.
What's he have to do before you're convinced, eat his enemies alive?
2. Even mentally ill characters need to have motivations that make sense.
Not true. Not everything is spelled out Nolan-style and tied in a nice little bow. People do things that don't make sense, and sometimes it's not even an external influence we can see and make out, but it's chemicals and biology (hey, if it's that way for humans, an imperfect clone surely could be worse off!)
In fact, the psychopathy displayed by Shinzon seems to fit the characterizations to a T. You know, following the set of rules they created for themselves, appearing even charming at times, etc, etc.