(Here you need to have really studied greek, or at least be willing to try or, the very least, use strongs

. Greek verbs and nouns take on Accusative, Genetive, Dative and nomanitive and Dative... please remember this with all Translations, then it also Might be male, female, or Neuter and then first person, 2nd person and 3rd person. singular or plural, oh and that excludes tenses) Thats why I still struggle with Greek :-)
Now I am going to address the NT first, as I dont have time to do all of the homework for the people on this site, as we all have to do the research. As I have stated before, don't just quote from a website, these guys have their own missgivings and some have some strange axe to grind.
It is easy to cut and paste, or link to a site... it is easy to think that these guys on the internet are actually all just telling the truth, but Bible study is not easy, it is something to be grappling with...
From this website are listed the following differences between the KJV and the NKJV. It is not an exhaustive list:
http://av1611.com/kjbp/articles/reynolds-nkjv.html
Titus 3:10-KJV reads, "A man that is an heretick...reject." NKJV and NIV change "heretick" to "divisive man"; RSV and NASV to "factious" man.
What is a heretic, but a person that spreads a divisive gospel. as the Gospel is to unite
Acts 4:27-KJV reads, "Thy holy child, Jesus." NKJV, NASV and RSV change "holy child" to "holy servant."
child3816
- pais -Perhaps from G3817; a boy (as often beaten with impunity), or (by analogy) a girl, and (generally) a child; specifically a slave or servant (especially a minister to a king; and by eminence to God): - child, maid (-en), (man) servant, son, young man.
Acts 8:9-KJV reads, "bewitched the people." NKJV and NASV change "bewitched" to "astonished." NIV and RSV change "bewitched" to "amazed."
bewitched1839
From G1537 and G2476; to put (stand) out of wits, that is, astound, or (reflexively) become astounded, insane: - amaze, be (make) astonished, be beside self (selves), bewitch, wonder.
Romans 1:25-KJV reads, "changed the truth of God into a lie." NKJV, NASV and NIV read "exchanged the truth of God for the lie" or "a lie."
into1722
A primary preposition denoting (fixed) position (in place, time or state), and (by implication) instrumentality (medially or constructively), that is, a relation of rest (intermediate between G1519 and G1537); “in”, at, (up-) on, by, etc.: - about, after, against, + almost, X altogether, among, X as, at, before, between, (here-) by (+ all means), for (. . . sake of), + give self wholly to, (here-) in (-to, -wardly), X mightily, (because) of, (up-) on, [open-] ly, X outwardly, one, X quickly, X shortly, [speedi-] ly, X that, X there (-in, -on), through (-out), (un-) to(-ward), under, when, where (-with), while, with (-in)
Romans 4:25-KJV reads, "Who was delivered for our offenses and was raised again for our justification." NKJV and NASV change "for" to "because of." (Even the NIV and RSV use the correct word, "for").
for1223
A primary preposition denoting the channel of an act; through (in very wide applications, local, causal or occasional). In composition it retains the same general import: - after, always, among, at, to avoid, because of (that), briefly, by, for (cause) . . . fore, from, in, by occasion of, of, by reason of, for sake, that, thereby, therefore, X though, through (-out), to, wherefore, with (-in). In composition it retains the same general import.
2 Corinthians 10:5-KJV reads, "Casting down imaginations." NKJV, NIV and RSV change "imaginations" to "arguments."
imaginations,3053
From G3049; computation, that is, (figuratively) reasoning (conscience, conceit): - imagination, thought.
Colossians 3:2-KJV reads, "Set your affection on things above." NKJV, NASV, NIV and RSV change "affection" to "mind."
1 Thessalonians 5:22-KJV reads, "Abstain from all appearance of evil." NKJV, NASV and RSV change "appearance" to "form."
appearance1491
From G1492; a view, that is, form (literally or figuratively): - appearance, fashion, shape, sight.
2 Timothy 2:15-KJV reads, "Study to shew thyself approved unto God." NKJV and NASV change "study" to "be diligent." NIV and RSV change "study" to "do your best."
Study4704
From G4710; to use speed, that is, to make effort, be prompt or earnest: - do (give) diligence, be diligent (forward), endeavour, labour, study.