I have decided to attempt learning Daf Yomi, and I hope to at least get through the first tractate (and hence the first Order, since only the first is part of Daf Yomi, as there was no Gemara written in the Babylonian Talmud for the rest of the Order Zeraim [Seeds, which deals largely with laws of Agriculture which largely applies only to the Land of Israel]. Today's daf (page) is page 7 (both sides) of Berachot (blessings). Until I get back to Atlanta, at which point I may begin ordering the new Koren Talmud, I have been learning it by listening to Rabbi Eliyahu Fink's shiur while following along on a printout of Shas Neharda (Moznaim Publishing, 2008), which is primarily as far as I can tell the Vilna Edition of the Talmud with some extra commentary both on the sides of the pages (in particular, when the Talmud references part of the Tanach (24 books of Hebrew bible), it quotes the entire verse with vowels) and presumably in the back as well.
Anyway, I was on the first side, about two thirds of the way down, when I ran into something that confused me. On the paper in front of me it said:
א"ר יוחנן משום ר' יוסי שלשה דברים בקש משה מלפני הקב"ה ונתן לו בקש שתשרה שכינה על ישראל ונתן לו שנאמר הלוא בלכתך עמנו בקש שלא תשרה שכינה על עובדי כוכבים שנאמר ונפלינו אני ועמך ונתן לו בקש להודיעו דרכיו של הקב"ה ונתן לו שנא' הודיעני נא את דרכיך
R. Yochanan further said in the name of R. Yosi: Moses requested three things from the Holy One, Blessed Be He, and He gave them to him. He requested that the Divine Presence would remain among the people of Israel and it was given, as it says, "Is it not that you go with us." He requested that the Divine Presence would not remain among the idolaters [literally: worshippers of the stars], as it says "So that we are distinguished, myself and your people". He asked to know the ways of the Holy One, Blessed Be He, and He gave it, as it says "Show me the ways"
However, Rav Fink read the bolded section as
בקש שלא תשרה שכינה על אומות העולם שנאמר ונפלינו אני ועמך ונתן לו
He requested that the Divine Presence would not remain among the nations of the world, as it says ...
I was confused, but then I remembered that manuscripts of the Talmud has more variants in the text than the Masoretic text of the Tanach (where they even tell you when something is supposed to be read as if it was spelled differently than the way it is printed). In fact, Googling the phrase as he read it led me to the Yalkut Shimoni, (see Wiki page) a medieval rabbinical compilation of aggadot on the Torah (difficult to translate, but legends/stories/exegesis on the text rather than halachot [laws]), quotes this section of the Talmud, with "nations of the world" instead of "idolaters." This version seems to present a somewhat more narrow version of things. By excluding only idolaters from having the Divine Presence among them, the Muslims, Sikhs and (possibly) the Christians [presumably at least the Unitarians] may still merit it, but by excluding the nations of the world, it would seem that only the Jewish people merit it.
But it may have been more than a variation. By this, I mean that fear of, or active participation of the non-Jewish censors may have played a role. An edition of the Babylonian Talmud printed in Amsterdam in 1714 has the bolded section as
בקש שלא תשרה שכינה רק על ישראל שנאמר ונפלינו אני ועמך ונתן לו
He requested that the Divine Presence should not stay anywhere except on the Jewish people" ...
An edition from Prague in 1728 has
בקש שלא תשרה שכינה אז רק על ישראל
He requested that the Divine Presence should not stay anywhere then except on the Jewish people" ...
This is interesting because it seems like they're saying it only applied then and didn't apply to the time it was printed (this was almost certainly the censors/out of fear.
And the first printed edition (there are older hand-written manuscripts but I don't think those can be found online although I could be wrong), by Daniel Bomberg in Venice in 1523? It has אומות העולם (nations of the world), just like in whatever edition Rav Fink was using. Unfortunately, I can't seem to find it in an edition he could plausibly be using; perhaps it's not in the Hebrewbooks library?
Update: Hebrew U has apparently scanned a whole bunch of Talmud manuscripts (site itself is Hebrew navigation only) in their Online Treasury of Talmud Manuscripts. Awesome!