If I understood your question, you are trying to connect the rejection of Jesus by the Jews of his day with what you propose to be a "flaw" of the Old Testament (OT) scriptures that they were reading.
I think it is illogical to judge the infallibility of any message given by God by the response of those rejecting it. By that logic, you can say that the Gospel of the Kingdom preached by the incarnate Son of God during his earthly ministry was "flawed" because it was rejected by the vast majority of the Jewish spiritual leaders who heard it preached.
That the OT was (and is) infallible can be seen in the testimony concerning it given by Jesus Himself when He was (no doubt) expected to "change" (or even "abolish") it in lieu of the miracles He performed (e.g., see people's testimony in John 7:31) and the divine authority He demonstrated in his teaching ministry (e.g., see people's testimony in Matthew 7:28-29). Precluding that train of thought, Jesus said (Matthew 5:17,18):
Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
It is worth noting that at the time that was said, none of the New Testament writing was to be in existence for at least another decade, and the term "the law and the prophets" used by the Lord in that quote would to my knowledge include the entirety of the Jewish Tanakh (or what Christians today would call the "Old Testament").
One of the verses that you give (2 Peter 1:21) summarizes the point regarding the infallibility of the Scriptures (specifically the OT ones) well:
For the prophecy came not in old time by the will of man: but holy men of God spake as they were moved by the Holy Ghost.
Does it not answer your question? If the "prophecy" (the entirety of the "Old Testament" can be inserted here) if fact came not by the will of man [...] but by the movement of the Holy Spirit in the holy men of God, would that not be another way of saying that what the prophets wrote down is "infallible" since it's the will of fallen man that can bring along error and falsehood.
Another way to think about it is if you believe Jesus was "infallible" and the "Old Testament" somehow was fallible, I think you would have seen the record of Jesus "correcting" the OT scriptures which He never did (correcting people's misunderstanding of it instead).
This is diverging from your question, but if you are trying to understand the reason for the rejection of the Jewish leaders (or any humans for that matter), you need to look no further than people's absence of saving faith as they hear God's message being preached to them. Chapters 5-8 of John's Gospel were really helpful to me on that account. I'll highlight just one portion below, but I'd recommend that you study that whole portion with prayer at length on your own as it's a critical point to understand if you are trying to see the "mechanics" of human rejection/acceptance of divine truth (John 8:42-47):
Jesus said to them [the Jews/Pharisees/teachers of the law], “If God were your Father, you would love me, for I have come here from God. I have not come on my own; God sent me. Why is my language not clear to you? Because you are unable to hear what I say. You belong to your father, the devil, and you want to carry out your father’s desires. He was a murderer from the beginning, not holding to the truth, for there is no truth in him. When he lies, he speaks his native language, for he is a liar and the father of lies. Yet because I tell the truth, you do not believe me! Can any of you prove me guilty of sin? If I am telling the truth, why don’t you believe me? Whoever belongs to God hears what God says. The reason you do not hear is that you do not belong to God.”