In Misquoting Jesus: The Story Behind Who Changed the Bible and Why Bart Ehrman examines the process by which the New Testament and other early Christian writings were copied and passed on. Since he earliest Christians were primarily poor and illiterate, the few literate Christians were expected to perform the scribal functions. Since they were not professional scribes, early copies were rife with copying errors.
Another problem with the process of copying is that there is no way to prevent the scribes from editing, either adding or removing from the document they were copying. So the documents we have contain both scribal copying errors and intentional changes. The task of the textual critic is to attempt determine which wording is the original.
Most errors are minor but there are certainly some known errors that effect important doctrinal views. The major Christian views such as the resurrection of Jesus, that he was sent by God and the he was born of a virgin are not in dispute. However, several changes have been made to support the divinity of Jesus, the notion of a triune God and the role of women were made.
So numerous and pervasive was the errors and changes that a pagan by the name of Celsus wrote a book challenging Christianity's legitimacy on that basis. Though Celsus' work is no longer available we do have a book, Contra Celsum, by the early church father Origen that quotes Celsus extensively.
In the early 18th century, when trying to develop a Greek John Mill made some startling discoveries. Amassing hundreds of manuscripts his discovered over thirty thousand variants, which now is closer to three hundred thousand. Mill's work was the first great work done in the field of textual criticism and, not surprisingly, created quite a stir. If biblical text cannot be trusted, leading apologists feared that this might be used by Catholics to claim superior authority of the church.
A Protestant by the name of Johann Wettstein made a significant discovery. 1 Tim. 3:16 in the King James version states in part "God was manifest in the flesh". However, Wettstein discovered in an old manuscript that the word used for the abbreviation for "God" was actually the word for "who" and this correction is made in the New American Standard Bible, "He who was revealed in the flesh."
A similar verse used to defend the divinity of Jesus is known as the Johannine Comma, 1 John 5:7-8 which reads "For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one. And there are three that bear witness in earth, the spirit, and the water, and the blood: and these three agree in one." However, this wording is completely different from which is present in the best manuscripts. Again the New American Standard Bible has the verses corrected "For there are three that testify: the Spirit and the water and the blood; and the three are in agreement."
Due to these and other changes made, Wettstein began to question the legitimacy of the concept of the triune god and the divinity of Jesus. Other changes were made to defend the faith including changing wording that might seem to support a "heresy" or adding wording to defend against a "heresy."
It is not impossible to discern what the original authors of the new testament books wrote. However, due to the amount of changes and not having the actual originals or even copies of the original but copies of copies of dozen times copied documents there are still argument among textual critics about what the originals said.
This of course does not mean that the basic story did not occur but it leads to great difficulty if you intend to claim the bible as inspired and that it has authority over what should be believed.