Who knows sixty-nine?
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The minimum number of dayanim at their posts in Yrushalayim at the time of the bais din hagadol.
23 at the entrance to the Har haBayis, 23 at the entrance to the Azara, the Lishkas haGazis's bais din had 71, but they didn't need to be there all the time. They could clock out if necessary, but at least 23 dayanim had to remain (San. 37a) (The set up is in San. 86b)
69 are the Shemittah and Yovel years that the Jewish People failed to observe during the period from their entry into Eretz Yisrael until the destruction of the first Beis Hamikdash. Correspondingly, they were sentenced to 69 years of exile, plus one more for the unfinished Shemittah cycle in which the Destruction itself took place (and which they would have violated too, if not for G-d moving up that event by two years in order to spare the Jewish People total destruction, G-d forbid).
(Rashi to Ez. 4:6)
69 is ס"ט. Contrary to a common misconception, this has nothing to do with "pure Sephardi" or "mud and dirt" or anything like that. It stands for סופו טוב (or an Aramaic version thereof), "may he come to a good end"; it's used by some Sephardic scholars folowing a living person's name as a blessing, much as Ashkenazim use "shlita."
A minor sanhedrin (23 in a town of 120) has 69 chachamim on deck (3 rows of 23).
If there was a 1 person majority to indict for a death penalty (you need 2) or if 1 of the dayanim did not know how to rule, we add 2 of the standbys (you can't have an even number on the B.D.) If this continues (e.g. the standbys split/don't know) you keep adding 2 until the bais din hits 71. (San. 37a) Really 48 would be enough, but the derech eretz was to have rows not bigger and not smaller than the actual bais din.