Rebbe did not actually have solid legal authority to do so under the normal rules of Jewish law, and instead invoked the verse, "There is a time to act for the Lord; they have nullified your Torah" (Tehillim 119:126). Recording the Oral Law is no less than a nullification of the Torah--yet if we wanted to have any Torah at all, there was no choice. Had the Oral Law not been written down, Torah would have been forgotten by the Jewish people. At times nullifying the Torah is, in fact, preserving the Torah.
Such was not the only radical innovation for which our Sages had very little basis, save for invoking the above referenced verse. They ordained that when greeting people, one should use the actual name of G-d (Brachot 63a). As religious life waned and many arose to challenge the authority of our Sages, it was felt that the name of G-d needed to be front and centre, thereby bringing honour to His name. The Mishnah actually reverses the verse, noting that since people were nullifying the Torah, it was a time to act for the Lord--and insist that we invoke His name.
That taking G-d's name in vain is a serious matter is the simple meaning of the Third Commandment. Our Sages expounded on the seriousness of using G-d's name frivolously by stating, "One who hears mention of G-d's name out of the mouth of his friend must excommunicate him, and if he does not excommunicate him, he himself will be excommunicated" (Nedarim 7b). G-d's name is the essence of holiness, and it must be used only when one beseeches G-d in prayer or communicates with Him in learning. To use it for other purposes is to make oneself worthy of excommunication.
To understand how severe excommunication is, we only need note that one who is excommunicated is not to be spoken to--as far as we are concerned, he is as good as dead. And upon physical death, he is not to be given burial rights nor is the family to sit shiva.
So important is the greeting of our fellow man that when doing so, all this is ignored and we invoke G-d's name.
When all is said and done, our tradition equates the greeting of our fellow man with that of greeting G-d. Man is, after all, created in the image of G-d. This concept underlies the halacha that one may, perhaps must, interrupt the recital of the shema in which we accept the yoke of heaven, in order to greet a fellow human being (Brachot 13a-14a). It is why Abraham told G-d to hold on while he went to welcome strangers into his home. It is the reason that it was said of Rav Yochanan ben Zackai that he was the first to greet all-- even idolaters in the marketplace (Brachot 17a). And it is the reason why we, too, must do the same. There is no better use of G-d's name than to use it to greet others. Shalom Aleichem!
 We have previously discussed how this innovation changed the halachic process to one in which the main role of later authorities is to interpret the teachings of those who came before them with much less allowance for disagreement with earlier authorities. See here.
 While it is obvious that the mention of G-d being referred to is G-d's name in vain the Gemara itself does not add that explanation referring rather to one who utters G-d's name, period. Even the mention of G-d's name where appropriate must be taken most seriously; the line between proper use of G-d's name and improper use is a thin one.
 The technical details of when exactly G-d's name may be pronounced when learning need not interest us here. See for example Yabiyah Omer, Orach Chaim, 3:18 for such a discussion.
 The term often used for excommunication, cherem, has the numerical value of 248, the number our rabbis said correspond to the limbs of the body. The cherem is a prayer that his bones should rot (see Moed Katan 17a).