Machlokes Rebbi Yossi V'Rabbanan (Shabbos 87)

The Rabbanan say that Rosh Chodesh Sivan was on Monday, Rebbi Yossi says it was on Sunday. I was wondering what the molad was. The sefer Itim L'Binah (Yosef Ginzburg, Warsaw, 5649, reprinted in Israel) says that the molad Nisan for that year was 5-2-332 (5 days, 2 hrs, 332 chalakim), so then molad Iyar was 6-15-45 and molad Sivan was 1-3-838. He has a long discussion to explain why Moshe Rabbeinu made Rosh Chodesh Nisan on Thursday, however basically, Hashem showed him the new moon during the day, and told him to be Me'kadaish the Chodesh then. Anyway, according to this, Rosh Chodesh Sivan should be on Monday (the new moon was not yet visible on Sunday night). However, this molad is the molad benoni, the molad amiti is different. For Nisan of that year, the molad amiti was Wed. at noon, (earlier than the molad beboni) , however, the sefer does not discuss when the molad of Sivan might have been.

B'He'elom Echod L'Rishus Echad (Shabbos 80a)

Rabbeinu Tam agrees with the Rach that the girsa is B'He'elom Echod Mai'Rishus Echad Chayov. What is the reason according to Rabbeinu Tam that Mai'Rishus Echad is required but not L'Rishus Echad? Rav Yaakov Kaminetsky z"l explains that if the two Chatzi Grogeres started in two different places and ended up in the same place, at the beginning they were nothing since they were not combined, only at the end did they become something Choshuv - he was Molid a new thing when he brought them together. But, if they began together, and he moved them to two different places, he moved something choshuv. He moved half of it to one place and half to another place, so he is Chayov.

Then, he asks, what is the reason of Rashi who learns that L'Rishus Echad Chayov? He explains that according to Rashi, the shiur of K'Grogeres is different from other shiurim of M'lacha on Shabbos. Other shiurim are about what is considerd Choshuv, less than the shiur is not Choshuv. However, the shiur of K'Grogeres is Halacha L'Moshe M'Sinai, so even though a smaller amount could be Choshuv, still the HL"M tells us that this is the shiur. Therefore, even though the two Chatzi Grogeres started in two different places, still they were Choshuv at the beginning. So, moving them to one place is not considered making a new thing (like Rabbeinu Tam), it is just considered to be moving two half shiurim and is mits'taref. He says that Rashi in other places can also be explained using this idea.

Hamechabeh V'hamavir (Shabbos 73a)

Why is Hamechabeh before Hamavir? Shouldn't it be the opposite, like Haboneh V'hasosair?

R' Yaakov Kaminetsky, z"l, in his sefer on the gemara, writes that the focus here is not about the benefit for the person, rather it is the benefit for the thing. Hamavir destroys the object, hamechabeh benefits and saves the object. See also Shabbos 106a and Rashi there.

Havara l'chaleik yatzas (Shabbos 70a)

The braisa quotes R' Nosson saying the source of the 39 melachos is from eile hadevarim and then R' Nosson says that havara was singled out to teach that you're chayav on each of the 39 melachos. Someone asked this morning if there was any connection between those two statements. I assumed that there really wasn't but then I saw that the Pnei Yehoshua explains that they are somewhat connected. He says that really R' Yosi fits in better with the pesukim. It makes more sense to say that havara was mentioned to teach that it's a lav and that's why it's written in that lashon. R' Nosson though says that it doesn't make sense to say that because the posuk earlier had just said that if you're over on a melacha you are chayav misa and that is the source that there are 39. So it's saying that if you are over on any of the 39 melachos you are chayav misa. It therefore can't be that havara is only a lav. So he's forced to say that it's was singled out to teach that you're chayav a separate chatas for each melacha.

Shitas Munbaz (Shabbos 68b)

I think that Munbaz' shita is a little confusing in the gemara. When I first read the gemara on 68b, I understood it to mean that Munbaz says you're only chayav a korban chatas if there is shigegas korban but not if there is shigegas lav or kareis. Here is the shakla v'tarya courtesy of Kollel Iyun Hadaf:

1. The case is, a baby was captured by Nochrim or a convert converted among Nochrim; he is also liable one Korban for eating blood, and one for Chelev, and one for idolatry [and for every other Chiyuv Chatas he transgressed].
2. Munvaz exempts.
3. Munvaz: [Regarding Shevu'as ha'Edus, one who transgresses] b'Mezid is called Chotei, just like Shogeg - just like Mezid knew [that he sinned], also Shogeg [is liable only if he once] knew.
4. R. Akiva: If so, you should say that just like Mezid knew at the time he sinned, also Shogeg who knows at the time he sins [is liable]!
5. Munvaz: Answer: Indeed, I say this! (This will be explained.)

The gemara will later explain that this is referring to shigegas korban. This sounds like Munvaz is saying that you are only chayav if you knew about it when you sinned and the only thing you didn't know was that you'd be chayav a korban if you did it b'shogeig. However, Rashi on the spot does say, "tchayvuhu gam b'zu chatas." I missed that when I read it though b/c to me it seems pashut pshat of the gemara is that you should only be chayav in that scenario just like line 3 from above. However, the gemara later makes it obvious that Rashi is correct. The gemara quotes the braisa on the bottom of 69a and attributes it to Munvaz where it says that you're chayav a chatas for shigegas korban and for shigegas lav. It fits in with the gemara on 68b but it just wasn't obvious to me when I first read it.

Me'ain Hameora (Shabbos 60b)

This is only tangentially related to today's daf but I thought it was interesting. I can't remember where I saw/heard this (it was a few years ago) but I'm not making it up and I apologize for not saying it in the person's name.

Why do women not wash mayim acharonim? It's not a mitzvas asay shehazman grama so they should be obligated just like men (assuming men are still obligated). There are some contemporary poskim who do say that they are chayavos but the vast majority of women do not wash mayim acharonim. I once saw an answer based on our daf. There are two reasons given for mayim acharonim. The more famous reason is because of melach sdomis. Tosafos says that doesn't apply anymore so based on that neither men or women should need it. However the gemara in Chulin (106a) also relates a story as a reason:

Mayim Acharonim caused a man to divorce his wife, he (Rav Dimi) was referring to 'Reuven', who saw 'Shimon', after having eaten a meal of lentils, deposit a purse-full of coins with his wife, before leaving the house without washing Mayim Acharonim. After waiting a while, he approached the wife and told her that Shimon had sent him to fetch the purse. When she asked for a Siman, he told her that they had eaten lentils, which he learned from the remains of the meal that surrounded Shimon's mouth, upon which she handed him the purse. Note, that Mayim Acharonim is also meant to wash the remains the meal from around the mouth. When her husband returned home and discovered what had happened, he divorced her.

I once heard that this is a second reason that the Chachamim instituted mayim acharonim and this reason might still apply today even if the melach sdomis reason doesn't apply anymore. If this is the only reason left then it will only be necessary in a situation that is me'ain hameora. So it would only be necessary if it's a man because it wasn't a woman eating in this story.