Gemara

(Beraisa - R. Yehudah): If a scribe needed to write Hash-m's name in a Sefer Torah, but thought that he needs to write 'Yehudah', and mistakenly omitted the 'Daled', he may trace the quill over the letters, to give Kedushah to the name.

Chachamim say, this is not an ideal writing of Hash-m's name.

Menachos 29b (Beraisa): If there are three mistakes on every Daf (column), they may be corrected; if there are four, Yiganez (it is buried).

Genizah is required only due to missing letters, but not if there are extra letters.

(Rav Kahana): This is because (extra letters can be erased, but) missing letters must be inserted between the lines, (if there are four on every Daf), the Sefer will look spotted.

Shabbos 103b (Beraisa): The following require Genizah (burial) of a Sefer Torah:

An open Parashah was written closed (regarding the space left between it and the next Parshah), or vice-versa;

Regular text was written like Shirah (parts of the lines were left blank), or if (text that should be written) Shirah was written normally;

Names of Hash-m were written in gold.

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.

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 Tur holds like the Rosh, that if one read in a Sefer Torah with any mistake, even something extra or missing, his Berachah was l'Vatalah.

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

Kesef Mishneh: Even one letter may not be written by heart. This is lest he add an extra letter or delete a letter, which disqualifies.

Rambam (Hilchos Sefer Torah 7:12): If there are three mistakes in every Daf of a Sefer Torah, it may be fixed. If there are four mistakes in every Daf, it requires Genizah.

Rambam (13): This is if words that should be written full were written deficient, and one writes the missing letters hanging between the lines. If words that should be written deficient were written full, even if there are many mistakes it may be fixed, for he scratches out the letters and does not hang them.

Rambam (8:3): If a Sefer Torah has mistakes regarding extra or missing letters, one can fix it. If one erred about the spacing of the Parshiyos and wrote open what should be closed or vice-versa, it is Pasul and cannot be fixed. The entire Daf must be removed.

Rashba (Teshuvos Chadashos 132): The Rambam learns from Shabbos 103b. He holds that 'Genizah' always means that it cannot be fixed; otherwise, it would say that it should be fixed. This is astounding! In Menachos it says that if there are three mistakes in every Daf, we fix them. If there are four, Yiganez. The Gemara said that this refers to missing letters, which can be added, but extra letters can be erased. Even missing letters can be fixed, by erasing and writing (smaller), since erasures do not disqualify! Rather, Yiganez until it is fixed.

Tashbatz (1:125): The Rashba holds that it says Yiganez only when it cannot be fixed without erasing. His proof from missing letters can be challenged. When one writes over erasures, it looks worse than putting letters between lines; four of these on each Daf disqualifies.

Poskim

Rema (OC 143:4): If a Sefer Torah has extra or missing (letters), we do not take out another, for our Sifrei Torah are not so accurate. Perhaps the next one will be no better!

Gra (OC 143:5): In a Teshuvah (Pe'er ha'Dor 9) the Rambam allows reading in a Sefer Torah with a mistake. We learned in Maseches Sofrim (2:1 and 3:7) that if one stopped in the middle of Hash-m's name or mixed letters, one may not read from it. Those who allow reading from such a Sefer say that one letter is Me'akev the Mitzvah to write a Torah, and Maseches Sofrim discusses when the entire Sefer is that way. L'Chatchilah, one should take out a new Sefer even for one mistake. B'Di'eved, we rely on Teshuvas ha'Rambam and Tosfos (who agrees). The Ikar is like it says in Maseches Sofrim; we do not distinguish Kashrus of the Sefer from reading it.

Mishnah Berurah (26): This refers to extra or missing 'Vovim' or 'Yudim' that do not change the meaning or pronunciation. For any other mistake we take out another Sefer Torah.

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.

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. The Halachah does not follow him.

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.

Teshuvas Yachin u'Boaz (1:24 DH Rabu): The Or Zaru'a said that if the leg of a Kuf was attached to the roof, one may erase the leg and write it again. However, he must ensure to not disqualify it, lest it look spotted, like it says about writing over Hash-m's name to be Mekadesh it. This is astounding. If so, all our Sifrei Torah are disqualified. All have letters written over erasures! No Posek challenged this. I say that writing over writing looks spotted, but writing over erasures does not.