QUESTION: The Mishnah says that a Chacham who made a woman prohibited to her husband by not annulling her Neder is not permitted to marry that woman, out of fear that he had improper motives when he prohibited her to her husband. However, if a woman did Mi'un or Chalitzah in front of the Chacham, then he may marry her, because Mi'un and Chalitzah may be done only in front of Beis Din of three Dayanim, and therefore there is no fear that all three Dayanim had improper motives when they permitted the woman to marry others.
Why does the Mishnah omit the most obvious case -- the case of a Get? The Mishnah should include the case of divorce together with Mi'un and Chalitzah and say that if a woman received her Get in front of a Chacham, she may marry him, because it was done only in front of a Beis Din, and an entire Beis Din is not suspected of having improper motives!
ANSWER: The PERISHAH (Even ha'Ezer 12:8) says that we see from this Mishnah that a Get does *not* have to be done in front of a Beis Din. It needs only be given in front of two witnesses. Since the Chacham contributes nothing to the efficacy of the Get, for it would take effect without him, the Mishnah has no need to include it in the cases in which it is the Chacham (or Beis Din) who causes the woman to become permitted to marry others.
Whether or not the procedure of a divorce must be executed in the presence of a Beis Din or not is the subject of considerable discussion among the Acharonim. Most notably, the NODA B'YEHUDAH (Even ha'Ezer 2:105, 114, 118) issues a novel ruling that a Get must be given over in front of a Beis Din. His ruling is based on several proofs. First, the OR ZARU'A rules that a Get may not be given at night. The Noda b'Yehudah asserts that the reason for this is because giving a Get requires a Beis Din, and since Beis Din does not convene at night, a Get cannot be given at night, but only during the day.
Second, he adduces support from the words of RASHI in Sanhedrin (2a, DH Mi'unin), who says that the reason Mi'un must be done in front of a Beis Din is because every Takanah enacted by the Rabanan was made with the same laws and conditions as the Halachah d'Oraisa upon which their Takanah was based. That is, when the Rabanan enacted the Takanah of Mi'un, they made it similar to the Halachah d'Oraisa of Get. Hence, Rashi is saying that Mi'un must be done in front of a Beis Din because a *Get* must be given over in front of Beis Din.
Third, others (see URIM V'TUMIM 9:2) cite the TARGUM YONASAN on the verse, "v'Kasav Lah Sefer Kerisus" -- "he shall write for her a deed of separation" (Devarim 24:1), who interprets the verse to says that "he shall write the Get *in front of Beis Din*."
These sources indicate that a divorce requires a Beis Din in order to take effect. However, the Acharonim point out that it does not seem to make sense that a Get should require a Beis Din, because there is an entire Masechta (Gitin) dealing with the topic of divorce, as well as many chapters on the topic in the Shulchan Aruch, and yet no one before the Noda b'Yehudah mentions that a Get needs to be done in Beis Din! On the contrary, the Gemara in a number of places makes the statement, "D you think that everyone who divorces his wife does so in front of Beis Din?" (Bava Basra 174b, Erchin 23a).
While the Noda b'Yehudah addresses these questions, the Acharonim reject his proofs that a Get should be done in front of Beis Din. First, they write that the reason a Get may not be given at night has nothing to do with the requirement of convening a Beis Din only during the daytime, but is due to other reasons (see BEIS SHMUEL EH 123).
Second, the PISCHEI TESHUVAH suggests that when Rashi in Sanhedrin says that Mi'un must be done in front of Beis Din because "k'Ein d'Oraisa Tikun," he does not mean that the Takanah of Mi'un is like the Halachah d'Oraisa of Get, but rather that it is like the Halachah d'Oraisa of a *Get Me'usah" -- a forced Get which the husband gives against his will. Such a Get must be given in front of Beis Din in order to be effective, as the Gemara in Gitin (88b) states. Alternatively, the MAHARAM SHIF in Sanhedrin there explains that Rashi means that the Takanah of Mi'un is like the Halachah d'Oraisa of *Chalitzah*, which requires a Beis Din. Mi'un, he says, more closely resembles Chalitzah than it does a Get, because it requires an action on the part of the woman, just like Chalitzah does, while in the process of the giving of a Get the woman is passive.
Third, the proof from the Targum Yonasan is not valid, the Acharonim point out, because the Targum does not mean that the Get must be given over in front of Beis Din. The Targum says only that the Get must be written in Beis Din. He means that a husband may not write any text of a deed of separation that he wants. Rather, he must write the exact text as prescribed by the Chachamim, and in order to do so accurately he must write the Get in Beis Din in order to receive instruction how to write it correctly..
HALACHAH: The Poskim discuss the ruling of the Noda b'Yehudah at length, but they reject it because his ruling is not mentioned in any of the earlier Poskim. Nevertheless, the practice is to be stringent and to require that a Get be done in front of Beis Din. This is in order to be stringent like the ruling of the Noda b'Yehudah, and, second, because there are so many complicated Halachos involved with the writing and giving over of a Get that it is important to do it in the presence of Beis Din in order to make sure that it is done properly.