What are the implications of "ve'Hayu ... le'Doroseichem"?
Sifri: It implies that Beis-Din are obligated to convene at all times, even when there is no Beis-Hamikdash - Dinei Mamonos, Dinei K'nasos and Malkos and the like. 1
But not Dinei Nefashos. See Torah Temimah, note 64.
Why does the Torah insert the words "be'Chol Moshvoseichem"?
Rashi (citing the Sifri): To teach us that as long as Sanhedrin Gedolah is operative in Eretz Yisrael, 1 Sanhedrin Ketanah operates in Chutz la'Aretz. 2
Ramban: To teach us that Beis-Din are obligated to convene at all times, even after the Churban and even in Galus, to judge fines, thefts, wounding and other monetary issues, and Dinim that concern Malkos. 3
See Sifsei Chachamim.
See Ramban's objection to this explanation.
Ramban (citing Sanhedrin, 52b and Mechilta): Based on the Pasuk in Devarim 17:9, they may only adjudicate with regard to the Dinim that involve Misas Beis-Din as long as the Kohanim are serving in the Beis-Hamikdash, but not after the Churban - because we Darshen "Chukas Mishpat" in this Pasuk only in connection with the Dinim of Misah - mentioned earlier in Pesukim 12 & 24 - See Ramban. See also Torah Temimah, note 65.