The phrase “perfect society” (societas perfecta in Latin) that is sometimes used to describe the Catholic Church is not meant to identify Catholics as if they were perfect.
It does not even mean that Catholics are somehow better than anyone else, since they’re not. All men and women are equal in terms of their human dignity, worth, and value in the eyes of God and the Church.
“Perfect” in this context does not refer to moral perfection. When an organization, association, or group provides everything the members need, it is considered a perfect society. Similarly, since the Church, founded by Christ Himself, has all seven sacraments (the fullness of grace), the totality of Divine Revelation as found in both sacred tradition and sacred scripture (fullness of truth), she perfectly provides for all the spiritual needs of all her members; they do not need to go to any other institution to have their spiritual needs met.
The federal government only provides for some of our temporal needs, so it cannot be called a perfect society. We need state and local governments in addition to federal. Even though a shopping mall may have every kind of store, restaurant, and bank available, it is not “perfect” since we need more than just clothes, food, and things. We also need schools for education and hospitals for healing.
The Church, however, has everything each member needs for his spiritual life and health. The teaching authority (magisterium), the sacraments and divine worship (liturgy), and the hierarchical structure give those who belong to the Church exactly and completely what they need, namely grace and truth.
Obviously, the leaders of the Church (from popes to pastors) have never been nor ever will be perfect or sinless. The members (from laity to clergy and religious) are not perfect, either. Yet the Church perfectly provides what her members need, maybe not what they want, but what they need. This is the only correct interpretation of the phrase “perfect society.”