Bad Mouth Strikes Again(1)

I recently took a management position. I have a co-worker who bad mouthed the previous person in my position and she is saying the same thing about me.
I found that in the past she wanted my position but passed it up because other co-workers convinced her that she would not like it. She says that I am making more errors although those in charge of monitoring errors, haven't noticed a difference.
My concern is that nobody is perfect and errors will occur. If she solely collects data on me and goes to my boss of course it will look bad.

How do I deal with this person?