Daf 141
1) If you carry out a child on Shabbos with a purse suspended around his neck, although you're exempt for carrying the child since he carries himself, but you're Chayiv for carrying the purse. We don't say that it's secondary to the person like we say by carrying him in a bed, that you're exempt for the bed too since it's secondary to him; for the bed is facilitating the man, and the purse isn't.
2) If so, we should say that a person carrying a child with a rock in his hand is carrying also the Muktza rock (similar to carrying the purse). The reason the Mishna allows carrying the child since we refer to a child that has a special attachment to his father, so they gave this dispensation so the child shouldn't become sick over it. However, they didn't allow it if he's carrying the coin Dinar since he might drop it, and you'll come to pick it up with your hands (and the most they gave a dispensation is carrying Muktza through the child, not handling the Muktza directly). [Rashi says; therefore, you shouldn't even hold a child's hand when he's holding a coin, because the same problem applies in this scenario too.]
3) However, if he carried out a corpse with a purse suspended around its neck, he's exempt. He doesn't need the corpse per se, so carrying it out is a Melacha Shein Tzricha L'gufo. [Rashi says the reason he's exempt for the purse; that he doesn't care for the purse now because of his terrible mental anguish. Tosfos explains the reason: since a purse is only necessary when carrying out a live child to entertain him, but it's not applicable by a dead one. Alternatively, he's exempt since it's an abnormal way to carry it out, on a dead body.]
Daf 142
4) If you have a stone in a basket, you need to tip it over to remove the stone before you move the basket. This is true even when it's also full with fruit even if the fruit will get ruined if they fall on the floor; still, you should shift the stone to be able to dump it out without dumping out the fruit. Although the fruit is more expensive, so the basket is not Bosis, but since it's possible to move the basket without moving the stones, you need to. However, if the stone is needed to stuff up a hole in the wall of the basket, then it becomes part of the basket and you can move it with the stone. [Tosfos asks: if so, why do we allow you to carry the child with the stone in his hand if you can knock it out of his hand? Tosfos answers: since we refer to a case that the child will cry if you do it. The reason why we don't say that the stone is secondary to the child (and it shouldn't be considered carrying Muktza at all) like we say here that it's secondary to the fruits in the basket, because you don't need to carry the child per se (but he needs you to carry him). Therefore the child is not as important in this carrying that the stone will be secondary to it.]
5) [Tosfos says: this implies that, if it wasn't for the fruit, the basket becomes a base to the stone and is Muktza. Therefore he asks: why don't we say that it's secondary to the basket without anything else in there just like we would say that a non-Jew's leftover wine in a cup would be secondary to the cup if it wasn't so stringent because it's forbidden to have pleasure from it.? Tosfos answers: leftover wine in a cup is very worthless that it's exceedingly easy to become secondary to the cup it's in.]
6) You can move Trumah Tamai in the same basket as Trumah Tehora if they're fruits that will be ruined if you dumped them all on the floor. However, that's only when the Tamai is on top and the Tahor is on the bottom. However, if it's the opposite and the Tahor are on top, you would need to carry the Tahor by themselves and leave the Tamai in the basket. [Tosfos explains: it's only when the Tahor are in little containers so they're easy to lift them by themselves, but we wouldn't require to pick them up by themselves if they're loose.] This is only if you need the fruit, but if you need the place of the basket (and you can't leave anything in its place), you're allowed to remove the whole basket with all the contents.
7) R' Yehuda says that, if Trumah fell into Chulin, if it has the ratio of one Trumah in a hundred Chulin, you're allowed to remove one of them to designate for Trumah (and it's not considered fixing). He holds like R' Shimon b. Elazar that one can eat it before separating by just looking at part of it (to make sure that it's not completely eaten so you can separate it later). Although R' Eliezer doesn't allow separating any Trumah since it looks like fixing (although you can eat this without fixing it), however, R' Yehuda argues with that point and holds that separating Trumah is not a problem unless it makes the rest of the produce fit to eat.
8) If you forgot a stone on a barrel, you need to tip the barrel to knock off the stone before carrying the barrel. However, if you left it there on purpose, the barrel is a base to the Muktza stone and is Muktza itself.
9) If it was between the barrels, (and you can't tip it in its place since it might break another barrel), you need to carry the barrel to a safe area and tip it over. This, that we don't allow moving the stone as is because it's like R' Shimon b. Gamliel who says that you need to deal with the Heter. As we see that he says that Beis Hillel only allowed separating on Yom Tov regularly in your lap or in a plate, taking the bad from the good when there is more good than bad, but when there is more bad than good, you should only remove the good and leave the bad. [Rashi's text and explanation: since it's a bigger bother to remove the bad. Although you might want to say that the barrel is compared to the case where there is more bad than good since there is a bigger bother to lift the barrel than to remove the stone; still, since you can't pour any wine anyhow without lifting the barrel, we consider as if it's more bad than good.
Tosfos text and explanation: the reason that you can take the bad from the good when there is more good since the bad is secondary to the good and Batul, so you can just pick out the bad and throw it away, (since it's like dealing with the good). However, if there is more bad, then it's not secondary to the good, so you need to deal with the good. However, the stone is not secondary to the barrel and is like having more bad than good since you can't take any wine until you remove the stone.]
10) This is all when you need to move the barrel since you need it, but if you need the place where it's on (and you can't just knock the stone onto that place), you may take the barrel with the stone on it until you place it down.
11) R' Yashiya, R' Yitzchok, and R' Yochanan hold that you may use it by placing a non-Muktza item, (like a child or bread), on the Muktza and carry them together. Mar Zutra says that's the Halacha if you forgot the Muktza in a bad place, but not if you purposely left it there. However, R' Ashi says that the Halacha is not like them even when forgotten, since they only allowed moving a corpse with a child or bread, but not any other Muktza.
12) Abaya placed a spoon on a sheath to move it, even though it was not really Muktza since it's fit for sitting, but he felt that an prominent person should be stringent. However, regularly, he wouldn't allow moving Muktza with a non-Muktza object like a child or bread.
13) Rava also placed a knife on a raw young dove, although it's edible raw, but he felt that a prominent person should be stringent.
14) That, which Rava needs the meat to be edible raw is because he holds like R' Yehuda that holds of Muktza, and since it's designated for humans, you can't move it because it's fit for animals. Although Rava allowed giving the spoiled guts of a duck to a cat on Yom Tov (although it was designated for humans and it's no longer fit for them); since he knew that it won't last until after Yom Tov for humans, he designated it from before Yom Tov for animals. [Tosfos explains: we must say that it was Shechted before Yom Tov so that the duck didn't need the guts. However, if it was Shechted on Yom Tov, since the duck needed the guts to stay alive, it was part of a food that's designated for humans, and it's like fruit pits that the fruit was still on coming into Shabbos that becomes Muktza (after the fruit is eaten) according to R' Yehuda.]
Daf 143
15) Beis Hillel allows removing bones and peels from a table. [Rashi says that it's completely inedible even to animals. Tosfos asks: if so, it would be Muktza even according to R' Shimon. Therefore, Tosfos explains: they're still fit for animals to eat.]
16) [Tosfos' text] Therefore, it's permitted to remove crumbs that are less than a Kazayis off the table since it's animal food. [This implies that you could destroy breadcrumbs directly and you don't need to worry that you're destroying fodder and not human food, not like Rashi's text that it's forbidden to destroy it because it says that you remove it from the table, and not that you throw it away.] The same applies by all things that become fodder on Shabbos, according to Beis Hillel and R' Shimon.
17) You can't wipe up a liquid with a sponge unless it has a handle. Even R' Shimon who usually permits unintended Melachos agree here since it's a P'sik Reisha, inevitable, that he'll squeeze.
18) However, you may move the sponge on Shabbos since it's a utensil. However, it's not susceptible to Tumah since it's not made of a material that's susceptible to Tumah.
19) If you have date pits from bad dates that you would only feed the dates to animals, then they're permitted, even to R' Yehuda, since it was always designated for an animal. However if the dates were originally good and designated for humans, and now the pits are just fit for animals, they're Muktza since whatever is designated for people is not considered designated to animals (and thus it was human food that became Nolad by turning into fodder). However, R' Shimon permits it since he doesn't hold of Nolad.
20) Shmuel moved the pits with bread. [Tosfos explains that he really held them not to be Muktza, but he was a prominent person, so he was stricter on himself.] This is because he held that you can use bread for any of your needs (and doesn't hold it to be disgraceful to the food).
21) Rava moved the pits with a basin of water. [Tosfos explains: despite Rava holding like R' Yehuda and these pits are actual Muktza, and we said earlier that we don't allow moving real Muktza with non-Muktza items unless they weren't really Muktza; we must differentiate that they allowed items that you couldn't practically move it from Friday, like these pits that are left before you when you eat the dates on Shabbos.]
22) R' Zeira threw them behind his bed when he ate the dates, but didn't allow them to pile up before him so that he can take it off later since it becomes disgusting, and they allow moving Muktza when it becomes disgusting (Geraf Shel Rei); since you're not allowed to L'chatchila make a Geraf on Shabbos so that you can move it.