Rambam - 1 Chapter a Day

The two witnesses may not, however, be related to each other (Sefer Me’irat Einayim 46:46). They may, however, both be related to the witnesses to the legal document (Rabbenu Nissim, as quoted by the Sefer Me’irat Einayim 46:46). Needless to say, a relative’s testimony is not accepted with regard to the signatures of the principals to a legal document (Siftei Cohen 46:47).
The Shulchan Aruch (Choshen Mishpat 46:18) quotes a difference of opinion among the Rabbis if it is acceptable for them to be related to the judges or not.

The rationale is that the two testimonies are considered to involve separate matters entirely. The father’s testimony concerns the subject mentioned in the promissory note, while the son’s testimony concerns his father’s signature and not the subject of the note. Hence one is not affected by the other.

For the testimony of two witnesses is necessary to validate each of the signatures, as stated in Halachah 3.

Alternatively, if each one is familiar with the signature of the other father, the document can be validated (Maharshal).

As Ketubot 28a explains, since the necessity for validating the authenticity of the signatures of the witnesses is a Rabbinic requirement, our Sages showed leniency and accepted testimony which is otherwise inadmissible (Radbaz; Kessef Mishneh). When, by contrast, Scriptural Law requires testimony, a witness must be acceptable both when he observes and when he delivers his testimony (see Chapter 14, Halachah 3).

The Shulchan Aruch (Choshen Mishpat 46:17) quotes a difference of opinion among the Rabbis if these concepts apply only with regard to the signatures of these three individuals - for these are the three signatures with which a person is most likely to be familiar, or if they apply with regard to any individual and the Rambam was merely citing the most likely examples.

If, however, both witnesses require this leniency, their testimony is unacceptable.

I.e., both witnesses testify to the validity of both signatures.

In which instance, his word is accepted, for he is testifying to the matters stated in the legal document, not validating his signature, as stated in the notes to Chapter 6, Halachah 2.

I.e., the effect of the witnesses’ testimony must be equally balanced, as implied by Deuteronomy 19:15: “The matter will be established on the basis of the testimony... of two witnesses.” Ketubot 21a states: “Half on the basis of one and half on the basis of the other.”

When the first witness testifies with regard to his own signature.

Or travels overseas (Sefer Me’irat Einayim 46:35).

The commentaries state that there is an advantage to signing on a shard, because afterwards, that shard could not be used for a legal document. If, however, he would sign on a piece of paper or parchment, that paper could be misappropriated and a legal document illicitly written on top of it. See Lechem Mishneh and others.

I.e., these witnesses will compare his signature on the shard to his signature on the legal document and on that basis, validate the signature on the legal document.

Since he is not testifying with regard to his own signature, that half of the money is not considered to be dependent upon his testimony.

Since the necessity for the validation of the signatures of the witnesses is a Rabbinic ordinance, our Sages were lenient and accepted the testimony even though it was delivered in the presence of only one judge (Kessef Mishneh).

Chapter 5, Halachah 9.

Thus they signed the validation in error. For at that time, the third judge was unable to validate the document.

If, however, the witnesses are alive, they certainly can be challenged. And if they are challenged and proven to be unacceptable as witnesses, the legal document is nullified and torn up [Ramah, (Choshen Mishpat 46:37)]. There are, however, other opinions which maintain that even if the witnesses are personally disqualified, their signatures on the legal document still have weight. See Sefer Me’irat Einayim 46:96.

Because of transgressions they committed. I.e., they attempt to nullify the effectiveness of the legal document with their testimony.

If, however, there is no proof to the validity of their signatures except the witnesses who maintain that they were unacceptable, the legal document is nullified and is torn up by the court [Shulchan Aruch (Choshen Mishpat 46:37)].

See Chapter 6, Halachah 3.

Since there is a pair of witnesses who testify that the legal document is invalid, the matter is considered as deadlocked. For whenever the testimony of two sets of witnesses contradicts each other, we consider the matter as unresolved.

Since the question is unresolved, we follow the principle: “Whenever a person seeks to expropriate money, the burden of proof is on him.” The bearer of the legal document must prove that it is valid. Since he cannot do so, because of the unresolved doubt described above, the defendant is allowed to retain possession of the funds. Nevertheless, if the claim involves movable property and the bearer of the document seizes property belonging to the defendant, the bearer may keep that property. The rationale is that the property is now in his possession and the original owner must sue to expropriate it. And he also is unable to prove his claim definitively [Tur, Ramah (Choshen Mishpat 46:37)].