Rambam - 1 Chapter a Day

Even if they both see the violator perform the transgression.

For capital punishment to be administered, a person must administer a warning and the transgressor must acknowledge it as stated in Hilchot Sanhedrin 12:2.

The standard version of Makkot, loc. cit., reads: “If [the witnesses] see the person administering the warning or the person administering the warning sees the witnesses.” It appears, however, that the Rambam’s version of the text stated “and” instead of “or.”

Despite the fact that they both saw the person commit the same transgression.

Makkot 6b derives this concept from the exegesis of Deuteronomy 17:6: “One should not die on the basis of the testimony of one witness.” Implied is that seeing the transgression one by one is also insufficient.

And if one of the witnesses is disqualified, the entire testimony is nullified, even though there are two acceptable witnesses who observed the transgression.

Witnesses who conspire and testify falsely. When their testimony is disproved, they are given the punishment that they intended to have given the intended victim.

This concept also applies with regard to testimony regarding prohibitions [Ramah (Choshen Mishpat 30:6)].

For both of them are testifying that he owes him money.
As the Shulchan Aruch (Choshen Mishpat 30:7) states, their testimony is combined only when the plaintiff claims to have given two loans. If, however, he claims to have given only one loan, their testimony is unacceptable, as evident from Chapter 3, Halachah 3.

In this instance, it is possible that the two witnesses are speaking about the same debt.

Here it appears that although the testimony was given afterwards, the loan concerning which he testifies must have been given before the first admission of the debt. Otherwise, the plaintiff must demand payment of two accounts as above (Kessef Mishneh).

And the borrower’s word is not accepted if he claims never to have made the loan.

For when an act of contract is performed, the witness would have the right to record his statements in a legal document at any time; see Hilchot Malveh vLoveh 23:5-6.

In his Kessef Mishneh, Rav Yosef Karo notes that the Tur (Choshen Mishpat 51) states that the document composed has the full status of a promissory note and can be used to expropriate landed property from people who purchased it from the borrower. The Kessef Mishneh differs and maintains that since neither the act of contract nor the original document was witnessed by two people, the document ultimately composed does not have the full power of a legal document and cannot be used to expropriate property. It is valuable only to negate the claim of the borrower if he asserts that he paid the debt. Significantly, in his Shulchan Aruch (Choshen Mishpat 51:1), Rav Yosef Karo rules according to the perspective of the Tur.
The Perishah (Choshen Mishpat 51) notes a difficulty with the Kessef Mishneh’s interpretation, for in Hilchot Malveh ViLoveh 14:10, the Rambam writes that even when only one witness signs a promissory note, we do not accept the borrower’s word if he claims to have repaid the debt. In resolution, the Perishah explains that in Hilchot Malveh ViLoveh, the borrower’s word is accepted if he takes an oath to support his claim, while in this halachah, he is not given that option.

Concerning a loan, an admission of debt, or the like.

Since each witness delivered his testimony before a court of law, it is acceptable. The courts, however, must come together as an entire body. It is not sufficient for some members of one court to join together with some members of the other. Nor is it sufficient for witnesses to testify that they heard these witnesses testify, for that would be indirect testimony which is unacceptable [Ramah (Choshen Mishpat 30:11)].

Bava Batra 165b interprets this as referring to an instance when witnesses testified concerning the validity of a promissory note, but the judges journeyed overseas before rendering a decision.

More specifically, one member of one court may join together with two members of another court. Bava Batra, loc. cit., and the Shulchan Aruch (Choshen Mishpat 30:12) speak of the witnesses offering testimony in three different courts. Thus the expression “one judge from each court can join together” is more appropriate.
The judges from the different courts can join together, because each court heard testimony from two witnesses and thus has enough evidence on which to base a ruling. In the first clause, by contrast, each court heard only the testimony of one witness and thus does not have sufficient evidence on which to base a ruling (Sefer Me’irat Einayim 30:34).

The witness will testify before the new court which will include one of the judges from the old court.

For all of the judges on the court rendering the decision did not hear two witnesses offer testimony concerning the debt. Instead, the witness is testifying concerning the debt and the judge is testifying that he heard witnesses testifying concerning the debt [Rashi (Ketubot 21a)].

From this preface, the Kessef Mishneh concludes that the principles the Rambam states apply only with regard to financial matters, and not with regard to questions concerning marriage and divorce, nor with regard to cases involving capital punishment.

Hilchot Toein ViNitan 15:2.

For a claim of possession to landed property to be established, witnesses must testify that the person benefited from the property for three consecutive years (Hilchot Toein ViNitan 11:2). In this instance, none of the witnesses can testify about the entire three year period. Hence their testimony is of no consequence.

For a person to be considered an adult, a woman of 12 years and one day and a man of 13 years and one day must manifest signs of physical maturity, i.e., they must have two pubic hairs. If they do not manifest such signs of maturity, they are still considered minors. This concept has manifold consequences with regard to the laws concerning financial matters. Needless to say, it is also significant with regard to the laws concerning marriage and divorce and the laws involving punishment for transgression (Kessef Mishneh).
Two witnesses must testify that the person in question did in fact manifest such signs of physical maturity. In the instance cited by the Rambam, the testimony of the witnesses is not acceptable, because neither of them gave testimony that could serve as the basis to say that the person manifested signs of physical maturity. They mentioned only half the required information. See also Chapter 21, Halachah 7, and notes.

For one hair in and of itself is of no consequence.

For each of them is delivering testimony that is, in and of itself, complete. Compare to Halachah 3 and Chapter 3, Halachah 3.