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1. There is a dispute about whether we read Parshas Shekalim when Rosh Chodesh Adar falls on a Friday.
2. There is a dispute about when we read Parshas Zachor when Purim is on Friday.
3. The Gemara discusses the four special Parshiyos and what is read from the Torah and from the Prophets for each one.
4. There is a dispute about whether the regular Torah reading is read during the weeks of these special Parshiyos.
5. The Mishnah discusses the Torah reading of all of the festivals.
A BIT MORE
1. Rav: We read it the Shabbos before Rosh Chodesh in order not to lessen the amount of time that the money-changers are present to assist with the donations of the Shekalim. Shmuel: We read it after Rosh Chodesh, since the money-changers anyway do not begin to provide their services on a Friday, but rather on the Sunday after Shabbos.
2. Rav: We read Parshas Zachor the Shabbos before Purim in order to remember our obligation regarding Amalek prior to observing the Mitzvos of Purim (which represent our victory over the descendants of Amalek). Shmuel: We read it after Purim, since there are people in walled cities who celebrate Purim on Shabbos (see Tashbatz 3:298 regarding how they celebrate).
3. The Four Parshiyos are (in order): Shekalim, Zachor, Parah, and ha'Chodesh. The Gemara discusses at length when they fall out each year.
4. Some say that only these Parshiyos are read, and others say that they are read in addition to the regular Torah readings (this is our custom today).
5. The Mishnah also speaks about the Torah readings for Chanukah, Purim, and the Ma'amados.
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