CLAIM 3) The words of the Mishnah and Talmud are clearly the words of men living in the 2nd-5th centuries CE and absent are the familiar Biblical formulae "And the Lord spoke unto Moses saying," and "Thus saith the Lord".
This argument would only be a challenge if the Mishna and / or Talmud claimed themselves to be prophetic texts... but they don't claim to be prophetic texts.
The Mishna and the Talmud claim to contain the legal rulings of the ancient Mosaic Court. The Tanakh ('old testament') constantly refers to these legislators and the divinely appointed authority given to them. (Examples will be given later in the clip.) The Tanakh does not only teach that prophets would be ordained by YHWH; it also teaches the positions of king, and of legislators, and of officers who inforce the legislation.
The Mishna was simply the first code, authorized by the Mosaic Court, which was intended only to serve as a GUIDE for public teaching of the Oral Instruction. It was intentionally very abbrivated, since the Mosaic Court was still functioning at the time of its composition, and the members of the Court did not yet feel an immediate threat of being overthrown by invading occupied forced.
The Mishna was not intended as an exhaustive codification of all the Oral Instruction, neither of the Oral Instruction from Sinai (halakha l-Mosha mi-sinai) or Oral Rabbinic Instruction (divrei sofrim) from the Mosaic Court.
CLAIM 4) The Rabbis claim that the "Oral Law" is the official interpretation of the Torah given on at Sinai. Yet if one actually looks at the Mishnah and Talmud they are full of the opinions of Rabbis who disagree with each other on almost every issue. The Rabbis explain that whenever there are such disagreements, "both opinions are the words of the living God." Karaites maintain that it is unreasonable to believe that God would contradict Himself.
There is more than one type of "Oral Law." Relatively few of the laws discussed in the Talmudic texts are considered by the Talmud to be Oral Instruction from Sinai. The majority of argumentation in the Talmudic texts is over what the proper Rabbinic law should be. Rabbinic law refers to the ajudication which Written Torah commands the Mosaic Court to practice, so as to instruct the people regarding how to correctly implement the 613 commandments of the Written Torah, and to give a final verdict on matters of dispute and disagreement among the population (Deu. 17:8-10; 2Ch. 19). The Written Torah gives recognition to the type of disagreements which appear in Talmudic Lit (examples later). Sometimes the argumentation is over a Biblical indication of a law, but not over the law itself. The variety of opinions among Karaites prove the practical necessity this religious Judaic-judicial system - the Almighty already touched on the issue long before Karaites lost knowledge of the solution. The variation of practice among modern day Orthodox Jews is also due to new situations that were not discussed in Talmudic Lit., which have arisen since the dismantlement of the Mosaic Court under the Roman occupation roughly 1,700 years ago. The Almighty has already promised by the hand of Isaiah the prophet that our judges will be restored as of old (Isa. 1:26).
"Both opinions are the words of the living 'G-d'" only in the context of theoritical application of the principles of Biblical interpretation, and only when these principles are properly applied; The phrase only means that when more than one legal understanding can be concluded by means of the interpretive principles, then both legal understandings are theoretically valid - BUT only the legal understanding which the majority of judges in the Mosaic Court agree upon becomes the binding and authoritative legal understanding. Karaites are correct that the Almighty does not contradict Himself; but humans understanding sometimes is sometimes a misunderstanding.