A student may excommunicate someone for slighting his honor.
A Torah Sage may adjudicate a monetary decision in his own favor if he is absolutely certain of the accuracy of his decision.
One should only learn Torah from a Rav that is akin to an angel of Hashem Yisbarach.
A father that hits an older son transgresses the prohibition of "Do not put a stumbling block in front of the blind."
A Torah sage may excommunicate himself and he may also revoke the excommunication.
All of the extenuating circumstances mentioned in the Mishnah that permit one to take a haircut on Chol ha'Mo'ed, only apply if there was no time to take a haircut prior to the Yom Tov. However a Nazir and a Metzora are an exception to this rule. (1)
According to Abba Shaul a mourner may take a haircut on Chol ha'Mo'ed under certain circumstances.(2)
According to the Tana of the Beraisa a Kohen may take a haircut on Chol ha'Mo'ed under certain circumstances.(3)
There is a dispute between Rebbi Yehudah and Rebbi Yosi whether it is permitted to cut nails on Chol ha'Mo'ed and during the mourning period.
A BIT MORE
1. A Nazir and a Metzora may take a haircut on Chol ha'Mo'ed even though they had time to do so prior to the Moed so as not to delay their Korbanos. They are not permitted to bring their Korbanos without first taking a haircut.
2. According to Abba Shaul a mourner may take a haircut on Chol ha'Mo'ed if the seventh day of the mourning period falls out on Shabbos. However the Rabanan hold that it is forbidden.
3. If the Mishmar of a Kohen ends during the Regel he may take a haircut on Chol ha'Mo'ed upon the completion of his Mishmar. The Tana of our Mishnah however is of the opinion that since all of the Kohanim have a share in the Korbanos of the Regel and the Lechem ha'Panim (show-bread), it is as if their Mishmar has not yet ended.
The Gemara says that if the eighth day of mourning falls out on Shabbos it is permitted to take a haircut on Erev Shabbos. The Yerushalmi asks how it is possible for the eighth day of mourning to fall out on Shabbos. The mourning period starts from the burial and if the eight day is on Shabbos, the mourning started from the previous Shabbos, and it is forbidden to bury a deceased on Shabbos. The Yerushalmi answers that it is possible for a person to be buried on Shabbos if a wild animal dragged the deceased into a grave, or if the burial was done on Bein ha'Shemashos (twilight) by means of a Nochri, or if a person died by drowning on Shabbos. (Meiri)
A father that hits an older son is excommunicated because it is a transgression of "Do not put a stumbling block in front of the blind." When the son reaches the age of twenty two or twenty four he is regarded as an older son. (Shulchan Aruch YD 240:20)
It is forbidden to hit a son once he reaches the age of twenty two; however the father is not excommunicated unless he hits the son after he reaches the age of twenty four. Once the son is married he is regarded as an older son even though he is not yet twenty two. (Pischei Teshuva)