Why was Mordechai appointed over Kinim?

Maharsha citing Bartenura: They require a great Chacham - Kinim and Pischei Nidah are Gufei Halachos.

Maharsha: A great Chacham is needed to understand every expression of one who comes with Kinim.

How does he open words and expound them?

Rashi: This is like he explained above (64b), the ladies who said Yamasi and Onasi.

Why do we require for the Sanhedrin Chachamim of great stature?

Rashi: It is so litigants will fear them, and not lie.

Why do we require for the Sanhedrin Chachamim who know witchcraft?

Rashi: If the litigant is a witch, and fire does not burn him, they will use witchcraft to kill him in any way possible.

Daf Al ha'Daf citing ha'Ben Yakir Li Efrayim (Teshuvah 37): What is the source that we may transgress an Isur Torah in order to kill one who is Chayav Misas Beis Din? In the Sugya of Ase Docheh Lo Sa'ase (Yevamos 6b), the Gemara wanted to infer that "Lo Seva'aru Esh" forbids burning a Bas Kohen on Shabbos, but if not for the verse, an Ase (execution) is Docheh a Lo Sa'ase with Kares (Melachah on Shabbos). We reject this; rather, a Kal va'Chomer would have taught that execution overrides Shabbos (Avodas ha'Mikdash overrides Shabbos. Execution overrides Avodah; all the more so execution overrides Shabbos!) Rashi holds that in a case of Hechsher Mitzvah (there is no other way to fulfill it, like here, that they can execute only via witchcraft), execution overrides Kares. Tosfos disagrees, therefore, he explained differently.

Tosfos citing Rav Hai Gaon: It is to know the law (when a witch is liable). This is like we say, that one who does an act is liable; one who does an illusion is exempt. R. Eliezer said, I teach 300 laws of planting gourds (Sanhedrin 68a). Also, we say that you may learn in order to understand and give rulings.

Does everyone on the Sanhedrin know all 70 languages?

Tosfos #1: Sanhedrin 17b implies that it suffices to have two who can speak (every language), and a third who understands it if he hears it. If four know every language, nothing is better than this!

Tosfos #2: Sanhedrin 17b discusses monetary cases. Here discusses capital cases [for which] 23 judges do not suffice. Some matters require 71 judges, e.g. Zaken Mamrei, judging a Shevet and Ir ha'Nidachas. Then, all must know all 70 languages.

Daf Al ha'Daf: Kli Chemdah (Shofetim 4) says that Tosfos' two answers argue about whether testimony about matters that require the Great Sanhedrin must be in front of the entire Sanhedrin, or it is enough to testify in front of three.

Why should Beis Din not hear testimony through a translator?

Rashi: Perhaps he will change the claims, and the Sanhedrin will give the wrong verdict.

What is the meaning of 'Bayil Lishnei and expounds them'?

Rashi: He mixes expressions and expounds them, e.g. Gagos Tzerifin and Ein Socher.

Maharsha: What is the source to expound that Mordechai is called Mordechai Bilshan? The verse implies that Bilshan is another Chacham! It seems that Mordechai should have been listed earlier in the verse, due to his esteem - "v'Gadol la'Yehudim v'Ratzuy l'Rov Echav'! (NOTE: This is unlike Megilah 16b, which infers that learning Torah is greater than saving lives, for initially Mordechai was listed fifth, and after the events of the Megilah, he is listed sixth! - PF) Rather, it is to expound Bayil Lishnei,

Why did R. Yochanan ben Zakai ask what is the source for the Baisusim? The Torah says to count seven weeks starting "mi'Macharas ha'Shabbos"!

Maharsha: Even though Baisusim do not accept Chazal's tradition that 'Shabbos' refers to Yom Tov, we should say that it refers to Yom Tov mentioned beforehand. Yom Tov of Rosh Hashanah is called "Shabason" (Vayikra 23:24) due to Shevisah (ceasing) from work. They answered that it is more reasonable to say that it refers to Shabbos Bereishis, for Moshe loved Yisrael, and wanted them to have a two-day Yom Tov.

Did they say that Moshe enacted by himself?

Tosfos: No; Hash-m consented.

Maharsha: Yes! This is why R. Yochanan ben Zakai called them fools. Surely Hash-m commanded when it is!

What is the contradiction between "Tisperu Chamishim Yom" and "Sheva Shabasos Temimos Tihyenah"?

Rashi: "Tisperu Chamishim Yom" (count until, but not including 50). It does not matter when in the week we start counting). "Sheva Shabasos Temimos Tihyenah" implies that seven full weeks (from Motzei Shabbos to Shabbos) must be counted!

How did R. Yochanan ben Zakai resolve the contradiction?

Rashi: Always, we start counting immediately after the first day of Yom Tov.) If Yom Tov is on Shabbos, the count of 49 days encompasses seven full weeks. If Yom Tov is any other day, there are not seven full weeks. We fulfill only "Tisperu Chamishim Yom".