Just finished studying with my Torah Mate. We recently began studying Chumash Devarim with Rashi and Gur Aryeh (the Maharal's super-commentary on Rashi) and we came to Deuteronomy 1:5, "On the other side of the Jordan in the land of Moab, Moses began clarifying this Torah, saying:" On the words "clarifying the Torah" Rashi comments (based on Medrash Tanchuma), "בשבעים לשון פרשה להם" - "He explained it to them in seventy languages."
This comment obviously needs explanation. Is it plausible that Moses actually got up and orally presented the Torah to the Jewish people in seventy different languages? How many languages did the Jewish people speak? Did Moshe get up and "explain the Torah" to them in languages that none of them understood? For that matter, the word used by Rashi is "פרשה" - "explained" - not translate!
So we started looking around. My chavrusa reminded me of the discussion of languages in Genesis 10:5, which, in turn, led us to look at the story of the Tower of Babel, in Genesis 11. One thing we noticed immediately is that, in the entire story of the confusion of the languages in Genesis 11, the Hebrew word "לשון" (lit. "tongue") is never used (unlike in Genesis 10:5). Instead, the word used for language in Genesis 11 is "שפה" (lit. "lip"). Rav Samson Raphael Hirsch, in his commentary on Genesis 10:5, and again on 11:1, writes that the word "שפה" designates actual language, whereas "לשון" refers to dialect.
This was useful, in that it at least showed us that the "שבעים לשון" - "seventy languages" - mentioned by Rashi need not refer to seventy distinct languages. However, it didn't really make much sense to say that he explained it to them in seventy different dialects either.
At this point, both of us were already thinking that these "seventy languages" probably were not "languages" at all, but seventy different modes of interpretation, related to the famous concept of "שבעים פנים לתורה" - "there are seventy facets to the Torah." But we were hesitant to give such an explanation on our own, without some support. Baruch Hashem, we found exactly what we were looking for in the commentary HaKesav VeHaKabbala (by Rabbi Yakov Tzvi Mecklenburg, d.1865):
Rashi, from the Sages, says, "He explained it to them in seventy languages." They don't mean foreign languages, for what benefit would that be to the Jews? ... Rather, it is the way of the Sages to refer to the intent of a statement by the term לשון..., and so here, with the "seventy languages", it means "seventy intended meanings", similar to the statement of the Sages elsewhere, "שבעים פנים לתורה" - "there are seventy facets to the Torah" - which refers to the inner intended meanings of the Torah, asides from the initial, simple meaning.