1) AGADAH: KNOWING WITH WHOM ONE IS EATING
QUESTION: The Beraisa teaches that the "Nekiyei ha'Da'as" (literally, the pure of mind, who are meticulous about their actions) of Yerushalayim would not participate in a meal unless they knew with whom they would be sitting.
The MARGOLIYOS HA'YAM writes that this Beraisa may shed light on the incident of Kamtza and Bar Kamtza (Gitin 56a). In that incident, why did the host insist that Bar Kamtza leave the house even after Bar Kamtza offered to pay for the entire feast? Moreover, why did Bar Kamtza hold the Rabanan who were present to be responsible as if they themselves threw him out?
ANSWER: The Margoliyos ha'Yam answers that the host knew that his invited guests, the Rabanan, agreed to participate only because they knew and respected the other people who were invited to the meal. The host felt that Bar Kamtza's presence would be insulting to all of the Rabanan who attended and they would refuse to attend any of his future meals. Bar Kamtza, in turn, held the Rabanan to be personally responsible for his eviction for the same reason. He felt that he was evicted only because the Rabanan were insulted by his presence.

23b----------------------------------------23b

2) INVALIDATING THE WITNESS OF ONE'S OPPONENT
QUESTION: Rebbi Meir in the Mishnah allows each litigant to invalidate a witness brought by his opponent. Rebbi Elazar explains that even according to Rebbi Meir, the litigant can invalidate his opponent's witness only if his words are supported by a second witness, and only if he rejects the witness based on "Pegam Mishpachah," a family blemish, by saying that the witness comes from a family of slaves (who are invalid to testify). When he does so, the litigant is not considered Noge'a b'Davar, because his testimony applies to the family in general, and not to the witness in particular. It is only a secondary consequence that the witness who is testifying against the litigant is invalidated.
How can Rebbi Meir allow a litigant to disqualify a witness in such a manner? Every litigant will disqualify those who testify against him in order to protect himself! Beis Din should relate only to the words of the witness who testifies along with the litigant, but since he is a single witness Beis Din should disregard his testimony.
ANSWER: Perhaps the Gemara relies on the fact that a person would not be so brazen as to disqualify an entire family as slaves merely in order to invalidate one witness. Because of this assumption, Beis Din does not suspect the litigant of lying. Still, however, Beis Din should not trust the litigant, because he is Noge'a b'Davar. The answer is that since the litigant's testimony is directed against the family, and the witness is disqualified only in an indirect manner, the litigant is not considered Noge'a b'Davar.
According to this approach, the litigant would not be believed to say that the witness testifying against him belongs to a family of known slaves and is not the son of his presumed parents. By testifying in such a manner, he is not disqualifying anyone else other than the witness testifying against him. This point indeed is implied by the words of the Gemara.
Also, according to this approach, a litigant should not be believed to testify that the family of his own witness (whom he has brought to testify on his behalf) is not a family of slaves and thus his witness is a valid witness, when the witness is otherwise suspected of being a slave. The litigant is believed only to disqualify, but not to validate, the family of a witness.
However, the Gemara in Kesuvos (22a) implies otherwise. The Gemara there says that when three judges sign together to confirm the validity of a document, and, later, one of the judges is suspected of being a slave, the remaining two judges may testify that the third judge is not a slave. The Gemara explains that although the other two judges are Noge'a b'Davar, since it is disgraceful for them to sign a ruling together with a slave, they nevertheless are believed because they are simply revealing a known fact ("Giluy Milsa b'Alma"). That is to say, since the truth eventually will become known, the judges would not lie about the status of their colleague.
It is clear from that Gemara that a person who is Noge'a b'Davar may testify even that a supporting witness is not a slave but is a valid witness.
Moreover, the Gemara there gives a different reason for why the litigant is not considered Noge'a b'Davar; it is because the status of this person -- whether or not he is a slave -- is a known fact and will easily be confirmed by others. This is not the reason given by the Gemara here.
The ARUCH LA'NER asks this second question. He answers that the two Gemaras are discussing two different types of testimony about a slave. In the case in Kesuvos, in which the third judge is suspected of being slave, the concern is that he is part of a known family of slaves. The other judges testify that his family is not known to be a family of slaves. This fact will easily be corroborated by neighbors and acquaintances of the family. In the Gemara here, in contrast, the litigant wants to disqualify the witness (who testified against him) by saying that he knows of a little-known fact of which others are not aware which would make the family of the witness into slaves. In such a case, the falsehood of the litigant's testimony will not be revealed, and therefore his testimony is suspect.
3) INVALIDATING A JUDGE
QUESTION: Rebbi Meir in the Mishnah allows each litigant to invalidate a witness brought by his opponent. Rebbi Elazar explains that even according to Rebbi Meir, the litigant can invalidate his opponent's witness only if his words are supported by a second witness, and only if he rejects the witness based on "Pegam Mishpachah," a family blemish, by saying that the witness comes from a family of slaves (who are invalid to testify). When he does so, the litigant is not considered Noge'a b'Davar, because his testimony applies to the family in general, and not to the witness in particular. It is only a secondary consequence that the witness who is testifying against the litigant is invalidated.
It seems that according to Rebbi Elazar, the beginning of the Mishnah can also be explained this way; a litigant can disqualify the judge that his opponent chooses by testifying together with another witness that the judge comes from a family of slaves. This indeed is how the TUR (CM 13) rules. The Tur writes that a litigant cannot disqualify a judge that his opponent chooses even when he is joined by a second witness and they testify about the family of the judge, because the Halachah follows the Rabanan and not Rebbi Meir.
However, RASHI (DH Amar Rebbi Elazar) writes that Rebbi Elazar is explaining only the end of the Mishnah. The beginning of the Mishnah must be explained in the way that the Gemara explains earlier (23a) -- that the appointed judges were only "Arka'os" and not "Mumchin," and the litigant disqualifies them merely by saying that he wants another court, and not by proving that the judges are slaves.
What forces Rashi to say that Rebbi Elazar's explanation does not apply to the beginning of the Mishnah, which discusses disqualifying the judges? (CHIDUSHEI HA'RAN)
ANSWERS:
(a) The LESHON LIMUDIM cited by the YAD DAVID explains that Rashi was forced to say this because of the Beraisa cited early in which Rebbi Meir says that the litigant may keep refusing to be judged by the judges that his opponent chooses until his opponent presents a judge who is a Mumcheh l'Rabim.
However, if this is true, then the same question may be asked on Ravin later in the Gemara (beginning of 24a), who says that the case in the beginning of the Mishnah as well is where the litigant is testifying with another person to disqualify a judge. Such testimony should be accepted even if the judge is a Mumcheh!
The answer must be, as the BINYAN SHLOMO suggests, that according to Ravin when the Rabanan say that a litigant cannot disqualify a judge if the judge is "Kasher or Mumcheh," they are teaching two different Halachos. The first is that if the judge is valid ("Kasher"), then even if he is "Arka'os," the litigant cannot refuse to be judged by him. Rebbi Meir argues and says that the litigant can refuse to be judged by that judge, and this is the subject of the Beraisa in which Rebbi Meir says that the litigant can refuse when the judge is not a Mumcheh. When the Rabanan say that if the judge is a Mumcheh, then the litigant cannot disqualify him, this implies that there is a case in which Rebbi Meir argues with the Rabanan and allows a person to disqualify even a Mumcheh. The second case is the case of Ravin, in which the litigant brings a second person to support his testimony.
The same answer can be applied according to Rebbi Elazar, and therefore it is not necessary for Rashi to say that the beginning of the Mishnah is not discussing a case in which the litigant disqualifies the judge by testifying that he is a slave.
(b) The RAN answers that if the beginning of the Mishnah is also discussing a case in which the litigant joins with a second witness to disqualify the family of the judge, then why does the Mishnah need to teach two separate cases -- one of disqualifying a judge, and one of disqualifying a witness? The Gemara itself asks a similar question with regard to why the Mishnah (24a) finds it necessary to teach a second time that Rebbi Meir allows a person to retract from accepting the testimony of an invalid witness. That is why Rashi prefers to explain that here the opinion of Rebbi Meir is not being stated twice.
(c) The TORAS CHAIM and BINYAN SHLOMO answer that Rashi maintains that even according to the Rabanan, a litigant can disqualify judges by testifying that they are invalid for any reason. The litigant is not considered Noge'a b'Davar since he knows that his opponent can simply bring the case before other judges, as Rashi says later (24a, DH Ika Bei Dina Achrina). (Rashi there might be following his own explanation earlier (23b, DH Nimtzes), where, according to his Girsa, the litigant is not considered Noge'a b'Davar as long as his opponent has other witnesses, even if the opponent did not obligate himself to bring those other witnesses. The same would apply to judges.) Therefore, the beginning of the Mishnah, in which the Rabanan say that a litigant cannot disqualify a judge, cannot be discussing a case in which the litigant testifies that the judge is not a valid judge (because if that were the case, then even the Rabanan would say that he is believed).
According to this approach, Rashi would disagree with the ruling of the Tur (cited above).