Wow, that would be a very lengthy prose. If you really are interested, there is a lot of good material on the subject from some very good Hebrew, Aramaic, and Greek scholars. Dr. John Ankerberg had a 8 or 9 show series revolving around KJV vs the modern translations with the editors of the NASB, NKJV, NIV, and adherents of the KJV only crowd. Very good discussion and many of the problems with the KJV were brought out.
One error that is pretty fragrant in 2 Thessalonians 2:3. the "falling away". That is not what the Greek says. Apostasia simply means departure. Without a text from what is being fallen away, departed from, distancing from, etc, to say "falling away" is taking liberties with the text that a translator should not do. This has been addressed by many top Greek Scholars like Dr. Kenneth Wuest, Dr. Andy Woods, Dr. Ed Hinson, et al. in their writings.
Since the actual Greek simply is departure, the context of the passage is laid out in verse one and two, the day of Christ and our gathering to Him, not our departing from Him. So the departure of Verse 3 is something other than a departing from the faith, falling away, etc. All the English translations prior to the KJV used "a departing", "departure", "the departing", etc. When the KJV translators got their hands on the text, they wrongly changed the meaning of the passage to "falling away" which conveys a very different idea than the Greek or the context of the passage does. Why they did that, I can speculate, but speculation doesn't matter. The Latin Vulgate, which the KJV translators had a great fondness for, also used dicessio, which is literally "departure" in the English and not "falling away".
The proper name of "Lucifer" is another and many KJV only folks love to jump on the other translations about this. Isaiah 14:12. Yet, "lucifer" is the Latin for Morning Star. Many of the newer translations actually use Morning Star, which is what the Hebrew says, much to the chagrin of the KJV only crowd. So by using "lucifer" by the KJV (and NKJV), it is implying that Satan (Hebrew..."adversary") has a literal name of Lucifer, which is not true. over 1000 years of the Latin Vulgate had tainted the KJV translators. They had a great fondness for the Vulgate.
Wow. Got me started. I don't want to write a dissertation here. Many scholars of much higher pay grade than me have outlined extensively the errors in the KJV. Go study and show thyself approved.
The KJV is a very good translation. It has stood the test of time. It expresses the main points of the scripture and the Gospel most adequately. One can trust the translation that they have one of the best. But like every translation, it does fall down in a few places. There is no perfect translation. Only the original writings are totally without flaw and direct from the Holy Spirit.