It's hard to find evidence of Calpurnia's weaknesses anywhere in To Kill a Mockingbird. She really is a mother figure for the children and is Atticus' counterpart in that sense. Aunt Alexandra comes in to fill that role at the end of Chapter 12, but she lacks Calpurnia's wisdom and of course Calpurnia's unique perspective of both white and black society. Calpurnia teaches the children and disciplines them, but leaves certain things to Atticus. This is, in small part, due to her role in their home and even though she works for Atticus, the most open-minded man in town, this is also due to - again, in small part - the racial history in Maycomb. However, when she defers to Atticus (for example, in Chapter 12 when Scout asks her what rape is), this is in large part because she respects Atticus and knows he will put it into proper perspective.
In Chapter 3, Calpurnia admonishes Scout for making fun of Walter. This is one of the first moments in the book when Scout gets a lesson about how certain social classes and races are not inherently better than others:
Don’t matter who they are, anybody sets foot in this house’s yo‘ comp’ny, and don’t you let me catch you remarkin’ on their ways like you was so high
and mighty! Yo‘ folks might be better’n the Cunninghams but it don’t count for nothin’ the
way you’re disgracin‘ ’em—.
Calpurnia teaches the children in words and by example how there can be a bridge between classes and races, even in a backward town like Maycomb. Calpurnia is that bridge. We see this firsthand when Cal takes the kids to her church. In Chapter 12, when Lula gives her grief for bringing white children to a black church, she says "It's the same God, ain't it?"