What is the significance of the fact that they saw the idols of the nations which they passed or among whom they resided?
Rashi (in Pasuk 17) and Ramban: Perhaps they became enamored by them 1 and decided in their hearts to adopt them and to ignore the B'ris, which is why Hashem finds it necessary to make Yisrael swear. 2
Seforno: Perhaps they became enamored by them and have decided in their hearts to go after them and to ignore the covenant. That is why Moshe stressed that they were all standing in front of Hashem who knows exactly what is in their hearts, and Whom they cannot therefore fool.
Ramban (in Pasuk 14): The idols of Egypt
How about the Mitzvos that the Chachamim introduced later - such as Mikra Megilah? How can they be included in the B'ris?
Shevu'os, 39a: They became included, when the Pasuk wrote in Esther, 9:27 "Kiymu Vekiblu ha'Yehudim", which implies that they accepted the Mitzvos that were introduced later together with those that they accepted at Har Sinai (and at Arvos Mo'av). 1
See Torah Temimah, note 11.
How can Moshe say to the current generation "You know how we dwelled in Egypt"?
Da'as Zekenim and Rosh: This proves that the decree [to die in the desert] was confined to men who were over twenty. 1
How can we extrapolate this? Perhaps only Levi'im and women survived from Egypt! It seems that we know that there was no decree against them only because they were not counted with Yisrael. If so, the same applies to Yisre'elim below twenty, who were not counted. (PF)