Is apostolic Tradition, apart from the Bible, inerrant or can it contain errors?
It is inerrant, and because it is inerrant, apostolic Tradition will never contradict the Bible, which is also inerrant. Human traditions may contain mistakes, but apostolic Tradition does not. Any teaching that the apostles authoritatively passed down to the Church is inerrant, irrespective of whether it is written down.
The key to telling which Traditions are apostolic and which are merely human is the same as they key to telling which writings are apostolic and which are merely human. It is the magisterium that recognizes the "canon" of apostolic Tradition, just as it recognized the canon of apostolic Scripture.
Scripture and Tradition are important because anything the apostles authoritatively passed down to the Church, whether written or not, is inerrant. The Catechism of the Catholic Church states,
Sacred Tradition and Sacred Scripture, then, are bound closely together . . . flowing out from the same divine well-spring, [they] come together in some fashion to form one thing and move towards the same goal.
As a result the Church, to whom the transmission and interpretation of Revelation is entrusted, "does not derive her certainty about all revealed truths from the holy Scriptures alone. Both Scripture and Tradition must be accepted and honored with equal sentiments of devotion and reverence." (CCC 80, 82, citing Vatican II, Dei Verbum 9)
Most of apostolic Tradition contains the same material that is found in apostolic Scripture, only in a different form. This makes the two useful for interpreting each other because they contain the same material phrased different ways.
For example, the doctrine of baptismal regeneration is found several places in Scripture, such as in John 3:5, where Jesus says, "Unless one is born of water and the Spirit, he cannot enter the kingdom of God." But because Jesus uses the metaphor for baptism, "born of water and the Spirit," many Protestants have tried to deny that it is a reference to baptism at all and have claimed that baptismal regeneration is false.
This is disproven through the apostolic Tradition preserved in the writings of the Church Fathers, who not only teach baptismal regeneration but also unanimously interpret John 3:5 as referring to baptism (see "The Fathers Know Best" column in the October 1994 issue of This Rock).