What is truly meant when it is said that Holy Scripture is 'inerrant' according to the Catholic Church? Granted that further research has been made in collecting a greater amount of old manuscripts of Scripture, certain realizations have been made about the bible that we currently use; there are some excerpts and passages that are not in older manuscripts, but rather are later add-ons (the two major examples being Mark 16 and John 5:7-8). The validity of these verses and the reliability of the Gospels is not to be discussed here. What is to be discussed is the Church's statement that the canonized Scripture used today is inerrant. What is truly meant by this word, and how is it reconciled with what scholars have shown us regarding these later additions to original manuscripts? Are there any specific thoughts from Catholic thinkers regarding this matter?

It should also be noted that I make it sound as though there are thousands of such meaningful and stunning additions to Scripture throughout the years, but such could not be further from the truth. The two major examples I listed are among the few meaningful additions that appear to have been intentionally added, but the additions themselves do not in themselves deter any accepted doctrine of the Church.
According to the Catholic Catechism,

we must acknowledge that the books of Scripture firmly, faithfully, and without error teach that truth which God, for the sake of our salvation, wished to see confided to the Sacred Scriptures.

This statement is purposely ambiguous, as there is debate among Catholic theologians about what inerrancy entails.  By saying the text is inerrant on matters God desired to communicate for our salvation, it opens up the possibility that the text contains incidental details that are not inerrant.  However, the ambiguity also allows that it is possible all details are also correct.  It just depends on what God chose to do, which humans can't know for sure.

Catholics United is a good example of a more strict interpretation within the Catholic Church:


Some have taught that the Scripture’s inerrancy is restricted only to “religious matters,” arguing that the Bible is without error only when it deals with matters of faith and morals. However, when it comes to non-religious matters of history or “background details,” these critics argue that God may have permitted human errors to exist alongside more important religious truths.
But this position has been refuted repeatedly by the Church because it necessarily limits God’s inspiration of the sacred texts.
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When it comes to matters of natural science, the Church teaches that the sacred authors did not necessarily intend to teach physics, astronomy, or chemistry. For example, when the Scriptures describe the sun as moving around the earth (cf. Ps. 19: 4-6; Eccles. 1:5), the sacred writer was not intending to give astronomy lessons. A literalistic approach would have to deny the modern scientific data showing that the earth revolves around the sun.
However, the writers were intending to report what appeared to their senses, and did so accurately.


While David Bennett offers a good defense of a less strict interpretation:


The early Fathers held that the Bible was inerrant... However, this is the case only when the Bible is properly understood, interpreted by the Church. This is inerrancy by ancient standards and not modern, fundamentalist standards. The early Fathers did not think that minor contradictions rendered the Bible errant, nor did they insist all stories were meant to be interpreted literally. For instance, the creation stories were often allegorized, interpreted in ways so as to prefigure Christ, or interpreted through the lens of the science of the day (or all three!). Thus St. Augustine could say each day in the Genesis creation story was equal to a thousand years, or that the science of the day should shape our understanding of the creation stories, without ever denying the divine inspiration of the Scriptures.
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Thus the view of the early Church is that the Bible is an accurate, God-inspired testimony, the written document accurately reporting the foundations of the faith, but not necessarily inerrant as defined by modern criteria, and the Old Testament is certainly not inerrant when exclusively interpreted literally.
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In conclusion, Catholics believe that the Bible is God-inspired, inerrant when interpreted correctly by the Church (and this is fluid to a degree, as science and other observations help us with this task), but not necessarily inerrant by the Protestant definition.