Gemara

(R. Ami): One may keep an uncorrected Sefer for 30 days, but no longer - "V'Al Tashken b'Ohalecha Avlah (do not let fraud dwell in your tent)."

Menachos 30a (Rav Sheshes): If one corrected even one letter of a Sefer, it is considered as if he wrote it.

Shabbos 104b (Beraisa): If one corrected one letter (on Shabbos), he is liable.

(Rava): Even if he removed the protrusion (in the top right corner) of a Dalet, thereby making it a Reish, he is liable.

Rishonim

Rif and Rosh (2:11): One may keep an uncorrected Sefer for 30 days, but no longer - "V''Al Tashken b'Ohalecha Avlah."

Note: In Hilchos Sefer Torah (after Menachos), the Rif and Rosh (3a and Siman 1) cite our Gemara to say 'an uncorrected Sefer Torah.'

Rosh: Rashi says that we discuss a Sefer Torah, Nevi'im or Kesuvim. Perhaps this is because in the days of R. Ami there were no other Seforim written. He does not exclude Seforim we have today. A mistake in a Gemara or Sifrei Poskim might cause an error between Isur and Heter or between liable and exempt. There is no greater Avlah than this!

Rebuttal (Yam Shel Shlomo 2:14): If Rashi did not want to exclude other Seforim, he would not have commented! Rather, one may keep Torah, Nevi'im and Kesuvim for 30 days before correcting them. One may not delay correcting a Gemara or Sefer ha'Poskim at all!

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.

Rosh: This is because the seller was forbidden to keep it uncorrected.

Rambam (Hilchos Sefer Torah 7:12): One may not keep an uncorrected Sefer Torah more than 30 days. After this, he must correct it or hide it away, but no longer - "V'Al Tashken..."

Hagahos Maimoniyos (10): Avi ha'Ezri says that this applies to Nevi'im and Kesuvim also. One who is careful even about Gemara will be blessed.

Me'iri (Kiryat Sefer 2:3 DH Shaninu b'Sheni): The Ri mi'Gash says that the Isur applies only to a Sefer Torah, lest one read in it b'Tzibur and bless on it. Some say that it applies even to Nevi'im, for we bless on reading the Haftorah. Some say that it applies to all Seforim, for mistakes can change the meaning. One should be careful about all Seforim. It is essential for a Sefer Torah, lest one bless on it. The Rambam obligates hiding a Sefer Torah if he does not correct it in time. This does not apply to other Seforim.

Noda bi'Yehudah (YD 2:174 DH Re'ayah Sheniyah): A Sefer that was not corrected after 30 days must be hidden away, lest it be used for Kri'as ha'Torah b'Tzibur. During the 30 days one may use it himself.

Poskim

Shulchan Aruch (YD 279:1): One may not keep an uncorrected Sefer Torah more than 30 days. Rather, he must correct it or hide it away.

Pischei Teshuvah (1): Yad Eliyahu says that if a Sefer Torah with mistakes became mixed with Kosher Seforim, it is Batel in the majority even though it is important. Many are lenient even when an error is found, just we do not follow their opinion. Here we permit l'Chatchilah, for it is a Sefek-Sefeka. (Perhaps the entire Sefer is Kosher. Even if it is not,) perhaps the mistake is not in the Chumash in which he reads. In pressed circumstances, this is permitted. However, one must make all efforts to find the mistake due to "Al Tishkon". The Chasam Sofer (276) disagrees. A Sefer Torah is like a nice portion fitting to honor someone, which is never Batel. Also, Bitul does not apply when the Isur can be detected, even if it is difficult. We learn from Bechoros 25b (if a Ba'al Mum became mixed with a herd, one must check all of them). However, if there is no time for this and there is no other Sefer Torah, we do not omit Kri'as ha'Torah with the Berachos. If they can check the entire Chumash from which they will read, they should do so.

Ketzos ha'Choshen (CM 35:4 DH v'Hinei): The Urim v'Tumim (46:131) disqualifies from testimony one who signed a Shtar Amanah (the lender received the document before the loan was given), or left a paid document or uncorrected Sefer in his house. This is wrong. These are forbidden, but one is not disqualified for them. Usury is a great Avlah, yet Tosfos does not disqualify witnesses who signed on a document for Ribis! Nevertheless, one is not believed to say that he did something improper.

Rema: The same applies to other Seforim. One may not correct any Sefer based on reasoning without a solid proof.

Darchei Moshe (1): R. Tam says that it is difficult to correct a Sefer based on reasoning, even if it seems that scribes changed the text because it was difficult to them. Early Chachamim imposed a Cherem against this:

Pischei Teshuvah (3): One may write the old text and one's suggested correction.

Birkei Yosef: Maharikash says that it suffices to write at the beginning that one corrected according to his reasoning. It is better to write both texts, so the reader can choose which is better. Sometimes the old text is correct!

Shulchan Aruch (545:1): It is forbidden to write on Chol ha'Mo'ed, even to fix one letter in a Sefer.

Kaf ha'Chayim (5): Even though one may not keep a uncorrected Sefer, since he should have corrected it before the Mo'ed, this is like leaving Melachah for the Mo'ed. Even if the mistake was discovered during the Mo'ed, fixing it is not a need of the Mo'ed.

Noda bi'Yehudah (YD 1:71 DH Emnam): We are not proficient about extra or missing letters; they do not disqualify. It is unlikely that all five Chumashim are truly Pesulim, so it suffices to hold a Sifrei Torah with a mistake for a Shevu'ah mid'Oraisa. When a mistake is found we put the Sefer to the side and do not use it in order to persuade the owner to fix it quickly and not transgress keeping it for 30 days.

Igros Moshe (YD 2:140 DH Ivra): The Noda bi'Yehudah (YD 1:74 DH v'Af) says that extra letters disqualify a Sefer Torah only if they are near a word and look like part of the word. Yad Sha'ul asks, if Hash-m's name was mistakenly repeated, we erase the latter one (Sofrim 5:1). According to the Noda bi'Yehudah, it is Kosher! This is not difficult, for one may not keep an uncorrected Sefer even if b'Di'eved it is Kosher. One would not erase the name from Tefilin or Mezuzos, for we do not read from them. However, the Halachah does not follow the Noda bi'Yehudah.

R. Akiva Eiger (2:36 DH uv'Ikar): The Isur to keep an uncorrected Sefer is when there is concern lest a word be misread, causing a misunderstanding. If the letter is misshapen, the only concern is in a Sefer Torah, lest one read b'Tzibur in another column, unaware of the mistake.

Chasam Sofer (OC 178 DH u'Mah she'Tzarich): One is liable for fixing (on Shabbos) a Dalet to make it a Reish. Rashi says that this fixes the Sefer and permits one to keep it, therefore this is Tikun (his act helped). The Rashba holds that one would not be liable for such Tikun. This forced him to say that the Sefer is Kosher for Kri'ah b'Tzibur.

Shevet ha'Levi (3:53 DH v'Chosav): To answer a contradiction in the Rashba, the Beis Meir (EH 125) said that the Rashba holds that removing the protrusion fixes the letter mid'Oraisa, but mid'Rabanan it is Pasul for it resembles Chak Tochos (writing a letter by erasing the inside). R. Akiva Eiger (1:37) disagrees. If so he would not be Chayav Misah! Since it is still forbidden to keep the Sefer due to "Al Tashken", the Melachah did not help! I say that this is Tikun, even if he may not keep it. Mid'Oraisa he fixed a letter; this is considered like writing a Sefer Torah, one who slaughters Kodshim b'Chutz for idolatry on Shabbos is liable for Chilul Shabbos, even though the meat is forbidden and Tamei, because it is no longer Ever Min ha'Chai (Pesachim 73a).