From what I learned, Jewish law is determinative in every matter, including mistakes, as it says: “According to all that they instruct you.” Make for yourself a rabbi — even if he is mistaken, you must obey him.
Ezra — maybe you can give examples like that, so we can learn from the factual errors you found.

Then you learned incorrectly.
1. Even if Jewish law is determinative, the question is what the Jewish law actually is.
2. Jewish law does not determine everything, only halakhic questions.
3. If there is a mistake, one does not necessarily have to obey. See Horayot 2: “one who errs in the commandment to obey the words of the sages.”
4. There is no shortage of factual errors in Jewish law (for example, the louse, and more).

Broadly speaking, it explicitly says that even if they tell you that right is left — listen to them. As I understand it, that includes Jewish laws.
3. I don’t understand what you mean that you don’t have to obey. That’s not a decisive answer.

4. I’m looking for examples of mistaken laws, not factual mistakes.

On the other hand, I don’t understand why the sages wrote factual errors.
Why don’t we today have the right to “correct” those errors in their words?

Nothing is written explicitly — not broadly speaking and not narrowly speaking. As is well known, there is a dispute here between the Babylonian Talmud, the Jerusalem Talmud, and Sifrei (“about right being right”), and I already mentioned the discussion at the beginning of Horayot regarding one who errs in the commandment to obey the words of the sages. In general, when there is an ambiguous saying like “right is left,” it can be interpreted in various ways. For example, it says that we do not expound the reason for a verse, but Tosafot HaRosh on Bava Metzia 90 writes that when the reason is clear, we do expound it. So if it says “right is left,” I would explain that if it is clear to you that it is right, there is no obligation to obey, even according to the version you quoted.
3. “You don’t have to obey” means there is no obligation to obey. In any case, there is also no logic in obeying if you have concluded that this is a mistake.
4. I mentioned the law of the louse on the Sabbath.

I’m even more confused, because the well-known explanation says: even if the sages are mistaken, even if they err unintentionally, even if they act intentionally — obey them,
“and you shall do according to what they instruct you”…

Anyone who transgresses the words of the sages is liable to death.

B. What does the reason have to do with truth? It sounds like if there is no reason and there is a mistake, then we would not obey their words.

C. According to what you’re saying, it comes out that it is an absolute sin to obey things that the sages told us to do if, in my opinion, they commanded something mistaken, or if it is clear to me that it is mistaken?

Moshe, as I wrote to you, throw the well-known explanation in the trash. The fact that it is well known does not mean that it is correct.

“Even if they err unintentionally and even if they act intentionally” was said only about sanctifying the month (there they derive from the verse “you” that mandatory authority was given to the Sanhedrin). On the contrary, from there there is proof that in other areas this is not so.

“One who transgresses the words of the sages is liable to death” (metaphorically, of course) in those places where it is forbidden to transgress. But where their words are void, this is not called transgressing their words.

B. I didn’t understand. When the mistake is factual, then from the outset their words are void (as with a mistaken sale or transaction — they did not say it on that basis). When there was no mistake originally, but reality changed, there are rules for changing Jewish law (and usually we require the great religious court: “a matter established by count requires another count to permit it”).

C. I see that you like decisiveness and absolute statements. In every message you come back to that.
I did not say that it is an absolute sin. There is room for defenses when you relied on the words of the sages even if they were said in error (at most, you are someone who errs in the commandment to obey the words of the sages). What I wrote is that there is no obligation to obey them. This matter depends on different approaches in the Horayot discussion that I mentioned, and this is not the place to expand.

For now I’ll ask this, then: why did they establish two-day holidays and new-moon days if only one day determines it? הרי they have authorization to make a mistake no matter what happens?!

Moshe, what exactly is the question? The authorization to err is for the Sanhedrin. And the reason they established two days is that in distant places they might miss the Sanhedrin’s determination. They do not have authorization to err. Beyond that, even the Sanhedrin does not want to err. It has authority, and its acts are valid if it made a mistake, but that does not mean they would not try to prevent mistakes.