Many characters in literature possess both positive and negative character traits. Sometimes, a character can be defined as dynamic--if their character changes over the course of the piece. Other times, a character can be defined as static (if they fail to change over the course of the piece).
In regards to Leonato, in William Shakespeare's play Much Ado About Nothing, he can be considered to have a couple major negative character traits.
First, Leonato is far too trusting (naive). He is easily persuaded by others (believing the noblemen based solely upon the fact they are nobles).
Second, Leonato's patience is rather lacking. For example, when the wedding between Hero and Claudio begins to stall, Leonato pushes it to be completed faster.
That being said, Leonato is also a static character--he fails to change. Many times, this characteristic (the failure to grow/change) proves to be the most negative.