Gemara

Mishnah: One who reads the Megilah by heart is not Yotzei.

One is Yotzei only if the Megilah is written in Ashuris, with ink, on parchment.

18a - Rava: We learn that one who read by heart was not Yotzei from a Gezeirah Shavah "Zechirah-Zechirah" from remembering Amalek, which must be in a Sefer.

Question: What is the source that Zechiras Amalek is reciting it? Perhaps it suffices to think about it!

Answer: It says "Remember, don't forget." Forgetting is in the heart, so "remember" must come to obligate reciting it.

18b - Beraisa #1: If the scribe omitted letters or verses, and the reader said them like a translator, he was Yotzei.

Contradiction (Beraisa #2): If letters were faded or torn:

If their image is recognizable, it is Kosher; if not, not.

Answer: If Miktzas (some) is faded or torn it is Kosher, but not if all is.

Mishnah: If one was writing, expounding or proofreading, he was Yotzei only if he intended.

Question: If he said each verse by memory before writing it he should not be Yotzei, for this is by heart!

Answer: Rather, he said each verse after writing it.

Question: But R. Chelbo said that (the Halachah follows the opinion that requires reading the entire Megilah, and) even the opinion that requires only from "Ish Yehudi" requires the entire Megilah to be written!

Answer: Rather, a complete Megilah was in front of him, and he read from it as he wrote.

Rishonim

Rif, Rambam (Hilchos Megilah 2:3) and Rosh (2:1): If one read the Megilah by heart he was not Yotzei.

Rif and Rosh (ibid.): A translator adds commentary by heart. Likewise, if one said a verse or letters of the Megilah by heart, he was Yotzei.

The Rif and Rosh (ibid.) bring the contradiction of Beraisos and the resolution.

Rambam (Hilchos Megilah 2:10): If letters were faded or torn:

If their image is recognizable, even if they are most of the Megilah, it is Kosher;

If their image is not recognizable, the Megilah is Kosher only if its majority is intact.

If the scribe omitted letters or verses, and the reader said them by heart, he was Yotzei.

Magid Mishnah (citing ha'Itur): Since it is Kosher if the minority was read by heart, the Tzibur may say some verses together with the Shali'ach Tzibur (the one reading from a Kosher Megilah).

Hagahos Maimoniyos (40): R. Shimshon learns from here that we are not concerned for Cheser and Yeser (a lacking or extra Vov and Yud that does not affect the pronunciation).

Poskim

Shulchan Aruch (OC 690:3): One must read the entire Megilah from a written Megilah. If he read it by heart he was not Yotzei. L'Chatchilah the entire Megilah must be written. B'Di'eved, if the scribe omitted words, even up to half, and the omitted words were read by heart, he was Yotzei.

Beis Yosef (DH u'Mah she'Chosav v'Davka): The Gemara answered the contradiction by distinguishing between Miktzas and totally (faded or torn). The Rambam explains that Miktzas means the minority, and 'totally' refers to the majority.

Question (Rashba 18b DH Lo, brought in Beis Yosef DH v'Chosav ha'Ran): The Gemara (18b) was Machshir if part is missing. On 19a it says that all require that the entire Megilah be written!

Answer (Rashba): The beginning and end must be written. Then, even if a minority in the middle is missing, it is a complete Sefer with errors. This is allowed because it is called Igeres. It must be complete because it is called Sefer.

Objection (Taz OC 690:3): R. Chelbo did not say that it is Me'akev that the entire Megilah be written. If so, the Rashba's question is not a question, and there is no source to distinguish whether or not a full matter is missing! The Gemara asked from one who wrote and recited it, for when he began to read only the first verse was written, which is clearly Pasul.

Levushei Serad (5): Our text of the Beis Yosef does not disqualify when a full matter is missing, only when the beginning or end is missing.

Answer (Magen Avraham 5): If R. Chelbo requires the entire Megilah be written l'Chatchilah, but it is not Me'akev, the Gemara would not have asked from his teaching! Since it asked, this shows that the Gemara knew that R. Chelbo's law is even b'Di'eved.

Beis Yosef (DH Kosav ha'Rashba and DH v'Zeh): If one holds a Pasul Megilah and reads along with the Shali'ach Tzibur, this is worse than two who read together, for he pays attention primarily to his own Kri'ah, and it is considered by heart. Therefore, verses that the Tzibur says out loud should be repeated by the Shali'ach Tzibur. One is Yotzei if the minority was said by heart, but that is b'Di'eved. We rebuke one who 'helps' the Shali'ach Tzibur by reading (out loud) by heart, lest people listen to him and not to the Shali'ach Tzibur.

Magen Avraham (6): This implies that one (the 'helper') can hear from the Shali'ach Tzibur even though he himself is reading.

Mishnah Berurah (5): Most say that if even one word was omitted, he was not Yotzei.

Kaf ha'Chayim (16,17): Some say that one who omitted a word was not Yotzei only if the omission changed the meaning, e.g. "These days will (not) pass from the Yehudim". Others disagree. If one missed something and is unsure whether or not this changed the meaning, he should read again without a Berachah.

Rema: If the Megilah is lacking at the beginning or the end, even a minority, one (who reads from it) is not Yotzei. Even in the middle, if an entire matter was omitted he is not Yotzei.

Sha'ar ha'Tziyon (10): Presumably we are not concerned if words in the first or last verse are missing. If the entire first or last verse is missing, perhaps it is Pasul.

Shulchan Aruch (ibid.): If more than half was omitted, even if the words were written but they were smudged and illegible, it is Pasul.