1. A gate requires a Mezuzah.
2. Synagogues do not always require Mezuzos according to Torah law.
3. A bathroom or place where people bathe does not require a Mezuzah.
4. A woman who lives alone is required to have a Mezuzah on her doorpost.
5. If a person is stingy, his house becomes susceptible to Tzara'as.
A BIT MORE
1. This is regardless of whether it is the gate of a house, yard, city, or country.
2. If a beadle or other person has a room in the synagogue where he resides, then the synagogue needs a Mezuzah. Rebbi Meir says that even if he does not live there, the synagogue needs a Mezuzah.
3. This is because it is denigrating for a Mezuzah to be at the opening of such an area.
4. The Torah emphasizes that this Mitzvah lengthens one's life. Women also need a blessing for long life, and therefore they are also obligated in the Mitzvah of Mezuzah.
5. If a person is asked to lend his items and he denies owning these items, Hashem causes his house to have Tzara'as. As a result, he is required to take everything out of his house, and everyone sees that he indeed owned these items and was merely being stingy.