Doesn’t the fact that stories found in new translations of the Bible that aren’t in older translations (i.e., John 7:53-8:11 and Mark 16:9-20) show that man can and has changed what was originally there?

What it points to is the power of oral tradition—the maintaining of historical traditions by accurately passing those traditions verbally from generation to generation. A great example is the story of the woman caught in adultery and how Jesus intervened on her behalf (John 8:1-11). It was included in the King James translation because the manuscripts those scholars had to work with included that particular story (it also was part of the Latin Vulgate translation that the Catholic church upholds). But as archaeology advanced and was able to find older manuscripts, they began to see that this story was either placed in other parts of John’s gospel (once even in Luke’s gospel) or left out entirely. The question becomes, What to do? As commentator Merrill C. Tenney explains in The Expositor’s Bible Commentary regarding this story, “It is absent from most of the older copies of the gospel that precede the sixth century and from the works of the earliest commentators. But this does not mean that it is unhistorical. Its coherence and spirit show that it was preserved from a very early time, and it accords well with the known character of Jesus.” Adds Dallas Seminary professor Edwin A. Blum in The Bible Knowledge Commentary regarding this story’s historicity, “Most commentators answer . . . yes. If this judgment is correct, then this is a rare extrabiblical authentic tradition about Jesus. John alluded to other things Jesus did (Jesus did many other things as well. If every one of them were written down, I suppose that even the whole world would not have room for the books that would be written—John 21:25) so this story may be one of those events.” As to where it is placed in John’s gospel, it actually fits well thematically; it fleshes out two of Jesus’ most important points in chapter 8: (1) You judge by human standards; I pass judgment on no one—Jesus Christ, John 8:15; and (2) Can any of you prove me guilty of sin? If I am telling the truth, why don’t you believe me?—Jesus Christ, John 8:46. Despite the trouble this woman was in, Jesus did not join the crowd of accusers, graciously following through on His words to Nicodemus: For God did not send his Son into the world to condemn the world, but to save the world through him—Jesus Christ, John 3:17. And he challenged those constantly testing and accusing Him of sin to bring proof—and they couldn’t. Quite an opposite picture of how quickly, when pressed by Jesus’ haunting response to their question—If any one of you is without sin, let him be the first to throw a stone at her”—Jesus Christ, John 8:7b.
The ending of Mark poses more serious problems. According to commentator Walter W. Wessel, “According to most contemporary scholars, the oldest and best attested manuscripts and versions, plus principles of textual criticism, tend in the direction of ending Mark with v.8. The external evidence seems to indicate that the Longer Ending (v. 9-20) was in circulation by the middle of the second century and was probably composed in the first half of the same century.” He goes on to mention serious differences between those verses and the rest of Mark in matters of vocabulary, style and content. His conclusion on these ending verses? “[T]he best solution seems to be that Mark did write an ending to his gospel but that it was lost in the early transmission of the text. The endings we now possess represent attempts by the church to supply what was obviously lacking.” Dallas Seminary New Testament professor Dr. John D. Grassmick tells of the possibility that, either by design or by being unable to finish his gospel, Mark’s gospel genuinely ends at v.8 and, later, oral traditions that captured the post-Resurrection stories of the other three gospels were included, possibly with the approval of the apostle John, who lived till the end of the first century. Such an addition would have been done without thought to literary style or grammar of Mark’s original work, but would have been thought to have captured the essence of his gospel. Very early on in the history of the church, these verses would have been granted the stamp of Scripture. Unfortunately, as Dr. Grassmick concludes, “A final conclusion to the problem cannot be reached on the basis of presently known data.”
Newer translations are actually more accurate as they have as their foundational documents older manuscripts, that is, manuscripts closer in time to the original documents. This makes them more accurate. When something like the adulterous woman story comes up, you find the integrity of the translators to be true in that they make note of the fact that, even if included in their translation, its documentary support makes it suspect. Truthful translators make every effort to run “agenda-free,” which means that, by design, translation teams come from many varied theological backgrounds to make agendas more difficult to surface, and therefore to maintain the integrity of the scriptures that Jesus assigned to it; when praying to God the Father in the Garden of Gethsemane, He simply said, [Y]our word is truth—Jesus Christ, John 17:17b.