Gemara

15a (Beraisa - R. Shimon): Had Moshe omitted even one letter of the Torah, it would not say "Lako'ach Es Sefer ha'Torah ha'Zeh"!

Gitin 60a: We learn from R. Yochanan that one may not read in the Beis ha'Keneses from a scroll containing only one of the five Chumashim.

(R. Yochanan): We may not read in the Beis ha'Keneses from a Sefer Torah missing a Yeri'ah (parchment).

Rejection: He disqualifies a deficient Sefer. Perhaps he allows a complete Sefer!

(Rabah and Rav Yosef): We may not read in it, for it is dishonorable to the Tzibur.

Megilah 8b (Mishnah): The only way in which Seforim differ from Tefilin and Mezuzos is that Seforim may be written in any language, but Tefilin and Mezuzos may be written only in Ashuris (Hebrew).

(Mishnah): Kisvei ha'Kodesh are not Metamei hands if Targum (words in Aramaic) were written in Hebrew.

9a: There is Targum in the Torah, i.e. "Yegar Sahadusa", but there is no Targum in Tefilin and Mezuzos!

Menachos 29a (Mishnah): The two Parshiyos in a Mezuzah are Me'akev each other. Even one Kesav (letter) is Me'akev.

(Rav Yehudah): Even the Kotz (a protrusion) of a Yud is Me'akev.

Maseches Sofrim (2:1): If one joined letters or interrupted in the middle of a Shem (word), one may not read in the Sefer.

Rishonim

Rif and Rosh (Hilchos Sefer Torah 2b and Siman 1) If one corrected even one letter of a Sefer, it is considered as if he wrote it.

Shiltei ha'Giborim (3a:1): The Mordechai (Megilah 2:793) says that if a Sefer is missing letters, words or a verse, we do not take out another. Even though there is no concern for disgracing the Sefer, since it really is Pasul, we are concerned for an unnecessary Berachah. Ri'az permits reading in an uncorrected Sefer unless a Yeri'ah is missing.

Hagahos Mahari (on Mordechai (2)): Nowadays everyone makes a Berachah before and after reading anyway, so we take out another Sefer.

Ran (Gitin 27b DH Mipnei): The Isur to read from a Chumash b'Tzibur is only due to honor of the Tzibur, for it appears to be poor. Therefore, if there is a mistake in one Chumash of a Sefer Torah, one may read in other Chumashim of it. Rabeinu said this l'Halachah, but not to act upon it.

Rambam (Hilchos Tefilin 1:2): If a Sefer Torah is missing one letter, it is Pasul.

Ran (Megilah 5b DH v'Chosav, citing the Ramban, and Kesef Mishneh explaining the Rambam): Just like one mistake disqualifies Tefilin and Mezuzos, the same applies to a Sefer Torah. A Mishnah says that the only difference between them is the languages and characters that are Kosher! R. Yochanan forbids reading from a Sefer missing a Yeri'ah. Perhaps this is when it is missing the last Yeri'ah. Surely, if it is missing even one letter in the middle, we may not read from it. The Gemara says that up to three mistakes in each Daf can be fixed. This implies that until it is fixed, it is Pasul.

Rebuttal (Ran): Indeed, just like one mistake disqualifies the Mitzvah of Tefilin and Mezuzos, it disqualifies the Mitzvah to write a Sefer Torah. We cannot learn from here to the Mitzvah of the Nevi'im to read from a Sefer Torah! If it is missing less than a Yeri'ah at the end it is Kosher, unlike Tefilin and Mezuzos! A Tosefta says that one is Yotzei if he read missing words by heart. Mistakes must be fixed, but one was Yotzei even if they were not fixed.

Defense (Gra OC 142:2): The Mishnah did not discuss the Mitzvah to write a Sefer Torah! Also, we establish the Mishnah to discuss Nevi'im and Kesuvim, even though the Gemara does not mention (a Mitzvah to write) them. One can say that the Mishnah discusses Tum'ah. However, whatever is not Metamei the hands is like a Chumash, and we do not read from it.

Beis Yosef (YD 279 DH v'Achar): In a Teshuvah (Pe'er ha'Dor 9) the Rambam allows reading in a Sefer Torah with a mistake. According to the Ran, we can resolve this with the Mishnah Torah. We follow the Ran, even though the Rashbatz challenged him.

Gra (OC 143:5): Teshuvas ha'Rambam learns from Gitin that only a missing Yeri'ah disqualifies. The Ramban says that this is only if it is at the end. The Rashba challenged this: mistakes at the beginning or end are more stringent, for then the deficiency is blatant! All the Poskim hold that even one mistake disqualifies. If not, the Gemara would not have said that it is obvious that one mistake disqualifies Tefilin. A Sefer Torah is Pasul if the names of Hash-m were written in gold (Shabbos 103b). This is merely a typical case. The same applies to other words, i.e. even a tiny minority of the Sefer. If a Shirah was written normally it is Pasul, even though this is less than a Yeri'ah.

Kesef Mishneh: Another proof for the Rambam is from Bava Basra, which says that a Sefer Torah missing one letter is not called a Sefer. R. Yochanan showed how Torah is different than Megilah. Even if a Megilah was missing several Yeri'os and they were read by heart, one was Yotzei. In a Sefer Torah, he was not Yotzei. Since absence of text disqualified, even one missing letter disqualifies.

Rosh (16): We may not read in the Beis ha'Keneses from a Sefer Torah missing a Yeri'ah. This is when all the Yeri'os were sewn together except for one. Even though all are in front of us, we may not read until all are joined.

Tosfos (9a DH Bishlomo): Why does Targum written in Hebrew Me'akev? Even if the words "Yagar Sahadusa" were omitted, the Sefer Torah would be Kosher! Rashi says that it is worse when it is written incorrectly than when it is not written at all. This is difficult. It seems that (it is not Me'akev;) the Mishnah merely teaches that it must be fixed.

Rebuttal (Gra, ibid.): This is difficult. Rather, it is Me'akev, and therefore, the Sefer is not Metamei, but one who read from a Pasul Sefer was Yotzei.

Poskim

Shulchan Aruch (OC 143:2): If each Chumash was written by itself, we do not read in it. They must be sewn together.

Bi'ur Halachah (DH Ein): Some say that the Tzibur can pardon their honor and read from it.

Rema (4): If one Chumash of a Sefer Torah has no mistakes, one may read in it, even if there are mistakes in the other Chumashim.

Bi'ur Halachah (DH Yesh): The Ran said this in the name of Rabeinu (the Rashba) l'Halachah, but not to act upon it. The Rashba said so only according to one answer. The custom is not to bless in such a case, but we do not protest against one who does.

Kaf ha'Chayim (44): The custom of Sefardiim is not to read in such a Sefer Torah, even in pressed circumstances

Shulchan Aruch (YD 278:4): If one of the Yeri'os was not sewn with the Sefer, even if it is with the Sefer, one may not read from the Sefer.