Gemara

146b (Mishnah): If one's clothes became soaked on the road, when he reaches the outer gate (of the entrance to the city, a guarded place), 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. (Rav forbids even in private!)

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.

Chulin 41b (Rava): The Mishnah permits to make a furrow near a pit and slaughter above the furrow, and the blood flows into the pit. One may not do so in the 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: Rav Nisim Gaon rules unlike Rav. A Beraisa (Chulin 41b) permits slaughtering above a furrow so the blood will flow into a pit, but not in Reshus ha'Rabim, lest he encourage the Tzedukim. This is no proof. Also here a Beraisa and Mishnah argue with Rav. Rav holds like the other Tana!

Note: In Chulin, also Rava holds unlike Rav, and he is Basra!

Rosh: If flax was dyed similarly to the color that wool is dyed, one may not make it a border for a wool garment (even if it is not connected in a way that the Isur of Shatnez applies) in a visible way, but one may do so for pillows and blankets. On Shabbos one may not pour into a sewage pipe that is covered for four Amos in Reshus ha'Rabim; a Beraisa permits pouring into a gutterpipe (that pours into the Chatzer), but not pipes that pour into Reshus ha'Rabim. It is permitted in winter, but a Beraisa permits only in a covert place.

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.

Tosfos (Chulin 110b DH Talis): Mid'Oraisa, a borrowed Talis is always exempt. Chachamim obligated it after 30 days, for it looks like his.

Poskim

Shulchan Aruch (OC 10:8): An open cape with four corners, if they fix in it clasps to make it like it is closed to exempt it from Tzitzis, this helps only if it is Kavu'a (permanently closed) at least half the length. Also, it must be Kavu'a below the belt, so the closed majority will be overtly visible. If not, it is forbidden due to Mar'is ha'Ayin.

Magen Avraham (12): One should not make hooks on a Talis Katan below the belt, for this is like closed. Terumas ha'Deshen (297) says that they are not considered closed regarding Kil'ayim unless they are bent so much that an act is needed to open them. Perhaps in any case it is forbidden due to Mar'is ha'Ayin.

R. Akiva Eiger (DH Lematah): The Levush says that even if it is long, he should not make hooks below the belt (even if the majority is open), due to Mar'is ha'Ayin, lest people say that he blessed improperly. Nezirus Shimshon permits.

R. Akiva Eiger (DH demi'Kol): If we are concerned for Mar'is ha'Ayin, we should be stringent also regarding Kil'ayim. However, we are not! This is even more difficult for the Levush, who is stringent lest people err to think that the hooks are totally closed, and that the majority is closed.

Mishnah Berurah (30): If one always wears a Talis Katan under his garments, and even when he goes in Reshus ha'Rabim it is concealed, Mar'is ha'Ayin does not apply (for also this is considered in private - R. Akiva Eiger DH Mishum).

Bi'ur Halachah (DH La'asosah): Acharonim argue about whether or not we are concerned for Mar'is ha'Ayin when the hooks are not bent too much. R. Akiva Eiger permits one who always wears the Talis Katan under his garments. Since we always have the Talis Katan under our garments, surely it is permitted.

Machatzis ha'Shekel (DH v'Efshar): The Magen Avraham says that we can equate Tzitzis and Sha'atnez regarding what is considered closed, and letter of the law one may make a Talis Katan closed below the belt with hooks that are not very bent. However, perhaps we are more stringent about Tzitzis than Sha'atnez regarding Mar'is ha'Ayin.

Minchas Yitzchak (10:99): The Bi'ur Halachah said that since we always have the Talis Katan under our garments, surely it is permitted. This would not apply to a Talis Gadol. However, it seems that the Bi'ur Halachah permits even without this (that it is always under our garments. It just made the Heter clearer.)

Bi'ur Halachah (DH Mishum): The Levush and Olas Tamid connote also garments that are mostly open must have an overt majority open. If it is a bare majority, people will think that he blessed l'Vatalah.

Rema (OC 10:12): Garments that people wear in Ashkenaz and Sefard, since the corners are not made to be two in front and two in back opposite each other, they are exempt from Tzitzis.

Beis Yosef (ibid.): In these lands people wear garments open in front and open slightly on the sides. They cut the two front corners, so the two back corners extend past them. Therefore, they are mostly closed (and therefore exempt from Tzitzis).

Bi'ur Halachah (DH Ho'il): The Pri Megadim says that a Sardak, which is totally cut in front and is cut on the left, it is exempt according to the Darchei Moshe. However, it is improper to totally exempt it, for letter of the law does not require two Tzitziyos in front and two in back. It is only l'Chatchilah. In order to obligate it in Tzitzis, one should make two corners on the right and two on the left, and a visible majority is open. If not, there will be Mar'is Ayin (it will seem that he blesses l'Vatalah).

Shulchan Aruch (17:2): A Tumtum and Androginus are obligated due to Safek. They wear a Talis without a Berachah.

Mishnah Berurah (6): The Beis Yosef explains that we are stringent about a Safek Torah. This connotes that if something is obligated only mid'Rabanan, e.g. a borrowed garment after 30 days, or it is half open and half closed, they may go in it without Tzitzis. The Pri Megadim says similarly. However, perhaps one should be stringent due to Mar'is ha'Ayin, like it says in 10:8.

Shulchan Aruch (YD 300:3): One may connect wool sleeves with knots, or hooks in linen chains with holes, and he inserts the knots or hooks in the holes, since they are loose and one can remove them with his finger without tearing the holes, even though he leaves them there permanently. If they are so tight that one cannot remove them without tearing the holes, this is connected, and it is forbidden.