(Mishnah): If any Zevach became mixed with Chata'os ha'Mesos (Chata'os that cannot be offered; they must be left to die) or with Shor ha'Niskal (it was sentenced to be stoned), and we do not know which is which), even if one was mixed with 10,000, all must die.

Ran (59b DH v'Ad): Heter is not Batel. It is the way of Isur to be Batel, but not Heter.

Beis She'arim (YD 364): Isur can be Batel because it is an existence. Heter is not an existence. It is merely the lack of Isur. A lack cannot be Batel. If so, a Pasul is not an existence. It is merely the lack of Kashrus, so it cannot be Batel.

Rema (OC 143:4): In pressed circumstances, if the Tzibur has only a Pasul Sefer Torah and cannot fix it, some permit reading in it b'Tzibur with Berachos. Some disqualify. If there is a complete Chumash without mistakes, one may be lenient to read in that Chumash.

Hilchos Ketanos (1:67): If a scribe forgot to be Mekadesh Azkaros (names of Hash-m), it is not Batel even in 1000, like it says in Zevachim. Perhaps in such a case, the Poskim would admit that the initial Kidush (of the first Azkarah) helps.

Beis Lechem Yehudah (YD 279): Hilchos Ketanos says that if one forgot to be Mekadesh an Azkarah, it is not Batel, even in 1000. If a mistake was found in a Sefer Torah, and it was forgotten, and it became mixed with another Sefer Torah, one must search again and again until finding the mistake. If he searched and did not find it, one can permit due to a Sefek-Sefeka (two doubts). The Rema says that in pressed circumstances, some permit reading b'Tzibur in a Pasul Sefer Torah with a Berachah. Perhaps this is the Halachah. Even if it is not, the Rema says in the name of the Ran that one may be lenient to read in a correct Chumash, even if other parts of the Sefer Torah have mistakes. Also, perhaps we read in the Sefer Torah without a mistake! It seems that one may be lenient even if he has only these two Sifrei Torah, and he needs to read in both of them, due to Sefek-Sefeka.

Yad Eliyahu (88): If a mistake was found in a Sefer Torah, and it was forgotten, and it became mixed with another Sefer Torah, I say that it is Batel in the majority. Do not say that it is important, so it is not Batel even in 1000. The Pesul is not important, only the Sefer itself is. There is no Isur to read in it. It has Kedushah, just the Tzibur must use a Kosher Sefer. Therefore, the Isur is Batel in the majority. This is unlike the case of Hilchos Ketanos. There, we knew the Sefer Torah with the Pesul. It cannot be Batel. Here we can say that the entire Sefer Torah is Kosher, and it is Batel in the majority. This is like salt full of blood. Even though salt is added for taste and it is not Batel if it itself was Asur, e.g. it was offered to idolatry, if it is Asur only due to blood absorbed in it, it is Batel. I say that even if there are only three Sifrei Torah and one must read from all of them on one Shabbos, it is permitted. We do not make the usual stringencies of dry mixtures. Also, many are lenient about mistake, even though this is not the custom. Also, perhaps the mistake is in a different Chumash. The Rema says that we may rely on this in pressed circumstances. Here, one may be lenient even not in pressed circumstances. However, due to the Isur to keep a Sefer with mistakes, one must be zealous to find the mistake.

Shirei Berachah (on Birkei Yosef YD 279): It seems that Yad Eliyahu overlooked Beis Lechem Yehudah.

Ha'aros on Birkei Yosef: We can also say that Bitul makes Isur as if it is not, but we have no source that Bitul b'Rov helps for Mitzvos to make something considered Lishmah. The Rashba says that when dry things mix, Bitul b'Rov teaches that what is in front of us is Heter. Therefore, one person may eat all three pieces one after the other. If Sifrei Torah became mixed, Bitul b'Rov can teach that any one is Kosher, but not that all are Kosher. We attribute to the majority when possible.

Chasam Sofer (YD 277): A Tzibur had a Sefer Torah with a mistake. Another Tzibur borrowed a Sefer Torah and returned it, and said that there was a mistake in it. It is not known if they borrowed the one known to have a mistake, or one of the others. Yad Eliyahu said that one Sefer Torah is Batel in two others, for the mistake is not an important matter (that is not Batel). Even if there were only three Sifrei Torah in all, he permits using all at once. The Magen Avraham (437:4) says that whenever there is Bitul b'Rov, even if one could check it, we rely on the majority. This is why we do not check for the 18 Treifos. I concluded that this is when there is no Chazakah against the Rov. However, whenever an Isur was mixed and it is possible to clarify and recognize it, it is not Batel. The Levush (brought in Taz 632:3) says that it can be Batel. He is totally wrong. Bechoros 25b says that R. Yosi cannot mean that one checks which is the Ba'al Mum to remove it, for surely, the first Tana would agree. We did not say that he discusses films in the eye and the animal was mixed with 1000 animals, i.e. and it is hard to check. Rather, if it is possible to check in any way (even if it is very hard) Bitul does not apply. The same applies to a mistake lost in a Sefer Torah. We also learn from there that here we cannot say that the one (mistake) that was lost is the one that was found, for mistakes in a Sefer Torah are more common than oxen goring each other. This is unlike the argument of Tana'im about one who checked and did not find. Here, we cannot say that a raven took it. Rather, we must say that he did not check well enough. Bitul b'Rov does not apply, even if he checked time after time and did not find it. Yad Eliyahu is difficult. He says that a Sefer Torah is important and it is not Batel, but since the Pesul is only due to the mistake, which is not important, it is Batel. He compares this to something Asur due to absorptions. This is astounding. This is like Chatichah ha'Re'uyah Lehiskaved (a nice portion fitting to honor someone) that absorbed a drop of milk. It is not Batel, even though the Isur is due to the milk. Since the piece itself becomes forbidden like Neveilah, so it is a Chatichah ha'Re'uyah Lehiskaved (which is not Batel). Here, due to the mistake, the Sefer is Pasul, or at least the Chumash it is in, for reading b'Tzibur. One may not rely on Yad Eliyahu.

Chasam Sofer: The Beis Lechem Yehudah is reasonable. After many searches, we may rely on a Sefek-Sefeka (two doubts). Perhaps this Sefer Torah is Kosher, and even if it is not, perhaps there is no mistake in the Chumash we read in now. It is easy to check one Chumash to verify that it has no mistake. Clearly, it is best to do so. If even one Chumash cannot be checked quickly, one should not omit Kri'as ha'Torah due to this. If checking Tzitzis will cause one to miss Tefilah b'Tzibur, this is like one who cannot check, and we rely on Chazakah (Magen Avraham 8:11). The same applies here. Also, whenever something is Batel mid'Oraisa, and due to importance it is not Batel mid'Rabanan, if one of the mixture one fell into the sea and we need not rule about it, we attribute that the Isur fell and permit the others two at a time (YD 110:7). Here, we do not say that the Sefer Torah in which the mistake was found, even though we do not say that this is the one known to have a mistake, since mistakes are common, in any case we do not rule about this Sefer any more. Therefore, we can say that also the first mistake was in it, and permit the others. Even though here we cannot use the others two at a time, we can join it to the Sefek-Sefeka mentioned above to permit if there is no time to check a Chumash.

Beis She'arim (YD 364): I do not understand what kind of mistake could be Batel. Bitul does not apply to a missing letter. Even regarding an extra letter, the Ran (Nedarim 52a) explained that since we hold that Min b'Mino and Olim (things offered on the Mizbe'ach) are not Mevatel each other, the Perush is not that the matter is Batel, rather, the Isur is Batel. Since the extra letter is there, how can we be Machshir the Sefer Torah?! Hilchos Ketanos says that if one was not Mekadesh an Azkarah, it is not Batel because a Sefer Torah is important. Even if it were not important, how can Bitul apply to a lack (of Kavanah)?!