Gemara

146b (Mishnah): If one's clothes became soaked on the road, when he reaches the outer gate, he spreads them out to dry in the sun, but not in front of people.

(Rav): Anything forbidden due to Mar'is ha'Ayin (suspicion) is forbidden even in private.

Question (Mishnah): He spreads them out in the sun, but not in front of people.

Answer: Tana'im argue about this;

(Beraisa #1): One may spread them to dry, but not in public;

R. Eliezer and R. Shimon forbid.

64b (Mishnah): [A donkey] may not go out with a bell, even if the clapper is plugged [because it looks like the owner takes it to sell it in the market].

(Beraisa): One may plug up the clapper of a bell on an animal's neck go with it in the Chatzer.

Question: This is unlike Rav! (We are concerned for Mar'is ha'Ayin only in Reshus ha'Rabim.)

Answer: Tana'im argue about this (in Beraisa #1).

Avodah Zarah 12a (Beraisa): If one's coins fell and scattered in front of idolatry, he may not bend to pick them up, lest it look like he bows to the idolatry. One may not put his mouth next to the mouth of a fountain (made in a person's image) to drink, lest it look like he kisses idolatry. If it will not be seen, these are permitted.

Suggestion: 'It will not be seen' means that no one will see him.

Rejection: Rav taught that anything forbidden due to suspicion, is forbidden even in private! Rather, it means that that it will not seem like he bows or kisses.

Kesuvos 60a (Beraisa - R. Marinus): A moaning child may suckle (from a goat's udder) on Shabbos.

This is because suckling is Mefarek (a derivative Melachah of Dash, i.e. extracting a food), done ki'Le'acher Yad (in an unskilled way. Normally, one milks by hand. Suckling is forbidden only mid'Rabanan.) Chachamim did not forbid it to one who is in pain.

(Rav Yosef): The Halachah follows R. Marinus.

(Beraisa - Nachum Ish Galya): If a gutter pipe became clogged (on Shabbos and the water is dripping into the house), one may covertly squash the clogging matter with his foot, without concern.

This is fixing a Keli ki'Le'acher Yad. Chachamim did not decree when this will cause a loss.

(Rav Yosef): The Halachah follows Nachum Ish Galya.

Yevamos 114a (Beraisa - Aba Sha'ul): We used to nurse from Tahor animals on Yom Tov.

Question: If there is a danger, it should be permitted even on Shabbos! If there is no danger, it should be forbidden even on Yom Tov!

Answer: The case is, they were in pain. He holds that nursing is Mefarek ki'Le'acher Yad, which is forbidden only mid'Rabanan. On Shabbos one is liable to stoning (for proper Melachah), therefore Chachamim decreed. Skilled Melachah on Yom Tov is only a Lav, so they did not decree to forbid one in pain.

Chulin 41b (Rava, and a Beraisa): One may make a furrow near a pit and slaughter above the furrow, and the blood flows into the pit, but not in Reshus ha'Rabim, lest it encourage the Tzedukim.

Rishonim

Rif and Rosh (62a and 22:9): Normally, we follow a Stam Mishnah against an argument in a Beraisa. However, in Avodah Zarah we asked from Rav (and answered). This shows that the Halachah follows Rav.

Rosh: We asked and answered similarly on 64b. Also, in Chulin, one who sees will realize that he wants to clean his yard, so there is no suspicion at all. There is no proof from Nachum. There, there is no suspicion of an Isur mid'Oraisa, for people see that he unclogs it in an unskillful way. The Yerushalmi (Kilayim 40b) asks the Bavli's questions and other Mishnayos and Beraisos against Rav, and does not answer.

Rambam (Hilchos Shabbos 22:20): If one's clothes became soaked, he may not spread them out to dry, even in his house. Whatever Chachamim forbade due to suspicion is forbidden even in private.

Rosh (4): Rav Yosef rules like Nachum. Aba Sha'ul said that they used to suckle from Tahor animals on Yom Tov. The Gemara concluded that this is Mefarek ki'Le'acher Yad. Chachamim forbade this on Shabbos, for which there is an Isur Skilah. On Yom Tov, which is only a Lav, they did not decree in a situation of pain. This is not difficult, for that is according to Aba Sha'ul. The Halachah does not follow him, for Rav Yosef rules like R. Marinus, who permits even on Shabbos. I saw some say that R. Marinus permits only due to pain that entails danger, to avoid a contradiction with Aba Sha'ul. This is a poor answer. If there were danger, why did we say that it is Mefarek ki'Le'acher Yad? Even total Melachah is permitted if there is danger! Some say that Aba Sha'ul discusses pain of hunger, like it says in Shevu'os (26b) 'if one vowed not to eat a loaf, and was in pain due to it...'

Ran (Beitzah 4b DH mi'Chalon and DH u'Mihu): In one version in the Gemara, Beis Hillel permit moving a ladder to an opening of a dovecote in Reshus ha'Yachid, but not in Reshus ha'Rabim, due to suspicion. The Rif omitted this, for he rules like Rav, that anything forbidden due to suspicion, is forbidden even in private. Rav Nisim Gaon brought proofs against Rav. On Chol ha'Mo'ed, one may make a laundry ditch or a coffin with the Mes in the Chatzer, but not in Reshus ha'Rabim (Mo'ed Katan 8b). I say that if these were difficult for Rav, the Gemara would have asked them, like it asked about coins scattered in front of idolatry. If one slaughters into a pit, onlookers will not say that he imitates idolaters. Rather, he wants his Chatzer to be clean. When the Mes is there, there is no suspicion! This is why the Yerushalmi permits even in the market if the Mes was famous. However, we can ask from 8b, in which R. Shimon ben Gamliel permits sawing boards in private in his house on Yom Tov [for a Mes]. According to Rav, it should be forbidden even in private!

Ran (DH v'Chalku): Some distinguish and say that when one will be suspected of doing something that is truly forbidden, we forbid even in private, e.g. moving a ladder or hanging clothes to dry. However, when they will think that he does an Isur, and really he does not (the action is actually permitted), it is permitted in private, e.g. the Aron or a clogged pipe. Since it is permitted, just people will think that it is forbidden, we forbid only in front of people. I disagree. These cases are not related to Rav's law. Rav teaches that anything totally permitted that Chachamim forbade only due to Mar'is ha'Ayin, is forbidden even in private. If we permit in private, he will do so in public, since it is permitted. He will say 'no one sees.' Similarly, Chachamim should be concerned lest someone see him in Reshus ha'Yachid, and (therefore they) totally forbid. Regarding an Aron, pipe and similar cases, the act is intrinsically forbidden. For a pressing need, Chachamim permitted a proper Melachah regarding an Aron, and a Melachah ki'Le'acher Yad regarding a pipe. Chachamim did not forbid (Melachah ki'Le'acher Yad) in place of a loss. Therefore, Chachamim permitted them only in private. Do not say that they should not permit them at all, for this is impossible. We are not concerned lest people come to do so in public, since the matter itself is forbidden.

Ran (61a DH Mema'achan): One may mash with his foot so the water will not drip into his house. Why do we permit covertly? Whenever Mar'is ha'Ayin is forbidden, this is even in private! I answer that when one who sees someone spreading laundry to dry will think that he laundered on Shabbos, therefore it is forbidden even in private. Here, one who sees will think that it is permitted, for he fixes ki'Le'acher Yad, and it is permitted to avoid a loss. Perhaps it is permitted not only covertly. If it cannot be done covertly, perhaps it is permitted even in public! However, it is best to be as covert as possible.

Question (Shiltei ha'Giborim 62a:1): A Beraisa permits an animal to go with a bell in the Chatzer, but not in Reshus ha'Rabim. The Gemara, Rashi and Tosfos connote that it is like the Stam Tana who permits spreading clothes to dry in private, but Rav forbids. Hagahos Ashri explicitly says so. Why do the Rif, Rambam, Rosh, Tur (and Shulchan Aruch) rule like the Beraisa? They rule like Rav!

Answer (Magen Avraham 301:56): The Beis Yosef (below) brings from Tosfos that we forbid in private only when there is suspicion of a Torah Isur. However, why didn't the Gemara give this answer for Rav? Perhaps Tosfos rejects the Sugya in Shabbos and rules like the Sugya in Kesuvos. (The latter Sugya did not challenge Rav, for it holds that Rav's law is only when there is concern for a Torah Isur - Eshel Avraham.)

Poskim

Shulchan Aruch (OC 336:9): If a gutter pipe became clogged (on Shabbos) with straw and grass, and the water is backing up onto the roof and dripping into the house), one may covertly squash the clogging matter with his foot. This is fixing through a Shinuy, since he uses only his foot. Chachamim did not decree when this will cause a loss.

Beis Yosef (DH Tzinur): Tosfos (Kesuvos 60a DH Mema'chan) says that whatever is forbidden due to Mar'is ha'Ayin is forbidden even in private only when there is suspicion of a Torah Isur, e.g. spreading laundry in the sun. The Ran [above] says similarly.

Mishnah Berurah (46): This refers to detached grass.

Mishnah Berurah (47): He mashes them and lowers them with his feet. The Me'iri forbids to remove them, even with his feet.

Question (Eliyahu Rabah 10): The Ran says that perhaps it is permitted even in public, if it cannot be done covertly. This is difficult, for the Ran in Beitzah connotes unlike this!

Bi'ur Halachah (DH b'Tzin'a): The Ran says that perhaps it is permitted even in public, if it cannot be done covertly. However, it is best to be as covert as possible. I say that also other Rishonim disagree, since they asked from Rav's law. If letter of the law it is permitted even in public, they have no question!

Kaf ha'Chayim (60): Eliyahu Rabah questioned this leniency of the Ran. Therefore, if it is impossible in private, he should do so through a Nochri.