- Shechitah by זר, etc., is valid, even לכתחילה
The third Perek begins on the previous Daf: כל הפסולין ששחטו – anyone disqualified from performing avodah who shechted, שחיטתן כשרה – their shechitah is valid, because shechitah is valid when performed by זרים, women, slaves, and tamei people, even for קדשי קדשים, provided the טמאים do not touch the meat. Therefore, they can invalidate a korban with מחשבה (such as חוץ לזמנו) during shechitah. The Mishnah’s language, "שחטו" – they shechted, implies that דיעבד אין – after [shechitah] was done, it is valid, but לכתחלה לא – initially, such people should not shecht. This is contradicted by a Baraisa which states that shechitah of זרים, etc., is כשרה: a passuk says “he” shall shecht the bull and “Aharon’s sons, the Kohanim” shall bring the blood, etc., implying: מקבלה ואילך מצות כהונה – from receiving the blood and onward is a commandment of Kehunah; לימד על השחיטה שכשרה בכל אדם – this teaches that shechitah is valid with any person!? The Gemara answers that although a זר may shecht even לכתחילה, the Mishnah expressed it as after the fact, because טמאים may not shecht לכתחילה, גזירה שמא יגעו בבשר – because of a decree that they may touch the meat and be מטמא it.
- ביאה במקצת שמה ביאה
עולא said in the name of Reish Lakish: טמא שהכניס ידו לפנים לוקה – a tamei person who put his hands into the עזרה] receives malkus, because the passuk says (about a tamei woman): בכל קדש לא תגע וגו' – she may not touch anything sacred [and she may not enter the Mikdash]. מקיש ביאה לנגיעה – This passuk compares entering [the Mikdash] to touching [kodashim]; מה נגיעה במקצת שמה נגיעה – Just as partial touching is considered touching (since normally one touches without his entire body), אף ביאה במקצת שמה ביאה – so too partial entry is considered entry. Therefore, if any part of a tamei person’s body enters the Mikdash, he incurs malkus for entering the Mikdash as a tamei.
- A recovering מצורע saw קרי just before Pesach (הואיל והותר לצרעתו הותר לקיריו)
עולא was challenged from a Baraisa about a מצורע whose eighth day of his purification process occurred on Erev Pesach. He saw קרי, and was טובל in a mikveh (becoming a טבול יום). Although ordinarily, a טבול יום may not enter הר הבית, this טבול יום may enter (to complete his purification and bring a korban pesach), because מוטב יבוא עשה שיש בו כרת וידחה עשה שאין בו כרת – it is better that an עשה (to bring a korban pesach) which carries a punishment of kares should come and override an עשה which does not carry kares, i.e., the prohibition for a בעל קרי to enter הר הבית. [Rebbe Yochanan says this prohibition is only דרבנן.] The Gemara asks, if ביאה במקצת שמה ביאה, how will the מצורע extend his hand into the עזרה for the blood of his אשם and oil to be placed onto his thumb? Since partially entering the עזרה is also an עשה שיש בו כרת, it should not be overridden to facilitate bringing a pesach!? Ulla answered that a מצורע is different: הואיל והותר לצרעתו הותר לקיריו – since he became permitted (to extend his thumbs into the עזרה) [despite] his צרעת, he is allowed to do so [despite] his [טומאת] קרי.