"The Rabbinic Tradition Concerning the "Alterations" Inserted Into the Greek Pentateuch and their Relation to the Original Text of the LXX" by Emanuel Tov is a party and a half.
Okay, not really, but it's cool once you get past the fact that you don't understand what you are reading because it's academia and difficult to wrap your head around on no sleep. (And come on, which student actually sleeps?)
For newbies, the LXX is the Septuagint. The Septuagint is the Greek version of the Hebrew Bible. If you're Jewish, you know Megillah 9a-b includes the story of 72 elders having been gathered by King Ptolemy, who placed them in 72 chambers and asked them to translate the Torah into Greek. Each scholar edited the text/ inserted certain variants identically.
Now, Emanuel Tov begins by telling you that various traditions (Megillah 9a, Yerushalmi Megillah 1,1,4, page 72a, Mek. Exod 12, 40; Midrash Hagadol Exodus 4,20; Abot de-R. Natan version B, chap 37; Sop. 1.7; Yalkut Shimoni Gen 3, Midrash Tanhuma Exodus para 22 and more) say 10, 11, 13, 15 or 18 alterations were made in the Greek translation of the Torah. You might think the shortest list is the "original formulation of the rabbinic tradition and that the longer list expanded it" (66) but this is not certain. The sources which state there were 13 or 15 alterations "are the most wide-spread and presumably reflect the central tradition." The lists having 16 or 18 alterations are the least reliable. 16 "came about as a result of the addition of biblical passages similar to those originally in the list, hence that list is secondary." When it comes to 18, it's influenced by "the list of 18 emendations of the scribes in the Hebrew text of the Bible" hence Tikkun Sofrim.
The base text is in Megillah and King Ptolemy's name is cited in all the sources. Now, these rabbinic texts suggest that the Greek translation was deliberately altered from the Hebrew. However, per the scholars, while "some of these differences do indeed stem from alteration" (72) others, which are in the majority, "stem from Hebrew variants, from translation technique and from an incorrect understanding of certain translation equivalents in the LXX" (72).
(As an interesting sidepoint, Christian tradition also focused on the differences between the Jewish and Greek Bibles, the Greek Bible being the Christian Bible from their point of view. However, in their case, a few Church Fathers "claimed the LXX reflects the true form of God's words, and that it was the Jews who had falsified them in their Bible" 72.)
Re: the list of alterations given in the Gemara, nine differ from the LXX and five agree with one passage being close. It could be that different translations stem from variant traditions that arose through the dissemination of the scrolls. There are no 2 scrolls nearly identical for any book of the LXX in pre-christian period. It seems that in many instances, changes were made to bring it more in line with Hebrew Bible, and so the list in the gemarah represents the original LXX.
The Background of the Differences between MT and the LXX Enumerated in the List (pages 82-83)
The lists in rabbinic literature speak of alterations that were inserted in the translation and it has already been stated above that at the time the sages regarded every difference between the Hebrew and Greek Pentateuch as a change inserted in the translation. In light of what has been stated above, the renewed discussion of the actual background of these differences now disregards the notion that they reflect alterations carried out by the translators). This renewed discussion is now made possible since the original text of the passages in the LXX (later corrected towards MT) has been reconstructed above.
The above-mentioned differences between the Hebrew Pentateuch and the LXX derive from the following factors: (a) translations deviating from MT based on Hebrew variant readings; (b) translations deviating from MT arising either from Hebrew variant readings or from exegesis; (c) exegetical translations; (d) Greek equivalents which were unjustifiably interpreted by rabbinic tradition as differences between the LXX and the Hebrew Pentateuch. This delineation raises most of the possibilities for the differences between MT and the LXX, both in the Pentateuch and in other books, aside from errors on the part of the translators and copyists.
The contents of lists of this type are largely a matter of chance, as is also the case with the list of the "emendations of the scribes" (see note 2). This list does not purport to represent the most conspicuous alterations and indeed the interested reader will easily find much more far-reaching differences between the LXX and MT, as for instance the order of chapters and subject matter at the end of Exod. On the other hand, what the biblical passages in the list have in common is that they pertain to some central issues. It is not hard to understand how post factum one would explain these differences as alterations (like the "emendations of the scribes", see note 2); however, this explanation holds true only in a few instances.
You'll have to read the whole article to see all the examples of the variants.