Gemara

12a (Abaye): In Tzur, Yisraelim leave pots on stovetops next to pots of Nochrim, and Chachamim are not concerned lest the Nochri put Neveilah into the Yisrael's pot when the Yisrael turned away.

34b: A boat loaded with Muryas entered the port of Ako. R. Aba said that we are not concerned lest Nochrim mixed in wine, because it came from a place where wine is four times as expensive as Muryas.

61a (Mishnah): If Reuven processed the wine of a Nochri (Tony) (to sell it to Yisraelim) and left it in Tony's house, which is open to a Reshus ha'Rabim, if there are Nochrim and Yisraelim in the city, the wine is permitted;

If there are only Nochrim in the city, it is permitted only if a Yisrael sits and guards it. It suffices if the Shomer (guard) goes in and out.

69a (Mishnah): If a Yisrael left a Nochri in a store with barrels of wine, even if he goes in and out, the wine is permitted. If he told him that he will not return for the time to pierce, seal and dry, it is forbidden;

Shimon ben Gamliel forbids if it is enough time to open, seal and dry.

A Yisrael and a Nochri were drinking wine together. They heard people calling that it is time to pray in the Beis ha'Keneses. The Yisrael left.

(Rava): The wine is permitted. At every moment, the Nochri fears lest the Yisrael remembered that he left his wine, and he is returning for it.

Chulin 3a (Abaye): The Mishnah teaches 'all may slaughter' - even Kusim (who converted for ulterior motives and did not observe all the Mitzvos). This is if a Yisrael supervises. If the Yisrael goes in and out, a Kusi may not slaughter.

Question (Rava): If the Yisrael goes in and out, he may slaughter!

(Mishnah): If one leaves a Nochri in his store, and a Yisrael goes in and out, (the wine) is permitted.

Objection: The Mishnah does not permit leaving a Nochri in his store. It just says that if one leaves a Nochri, the wine is permitted! Rather, Rava asked from the following Mishnah.

(Mishnah): The Shomer need not sit and watch the whole time. If he goes in and out, this suffices.

(Rava): Rather, the Mishnah teaches 'all may slaughter' - even a Kusi. This is only if a Yisrael goes in and out;

Rishonim

Rosh (1:9): The Hava Amina to be concerned for switching is only if the Nochri would benefit. We are not concerned lest Nochrim mixed in wine in order to make Yisrael sin, unless they would benefit. We rely on this to leave pots with slaves when we go to the Beis ha'Keneses. Also, this is like going in and out. It is proper for one with Yir'as Shamayim to be stringent, for sometimes problems occur. Also, in order to improve her portion, she adds milk to the pot.

Tosfos (12a DH v'Shadi): The Chidush is that in Tzur we are not concerned lest a Nochri put lean Neveilah in the Yisrael's pot and take the Yisrael's fatty meat, to profit. We would not be concerned lest he switched without any profit even if the Yisrael went far away. We learn from 34b. There is no concern lest they mixed in wine in a place where wine is more expensive. This is why we leave our pots with Nochri slaves without concern lest they put Isur inside.

Poskim

Shulchan Aruch (YD 118:10): If one leaves a Nochri in his house, and there are things that have even an Isur Torah if they are switched, if he goes in and out, or even if he delayed greatly but he did not tell the Nochri that he will delay, it is permitted. We are not concerned lest he switched, even if he would profit through switching. This is if he (the Nochri) did not close the house, for at every moment the Nochri fears lest the owner come and see him. If he would not profit through switching, it is permitted in every case. We are not concerned lest he switched to make the Yisrael transgress, since he does not benefit from this.

Beis Yosef (DH ha'Meni'ach): The Rashba learns from Chulin that a Yisrael going in and out permits even for a matter in the hands of the Nochri. The Halachah follows Rava. If the Yisrael told him that he will not return for a while, it is forbidden.

Beis Yosef (DH u'Mah she'Chosav): In Siman 129, the Tur explains that if the Nochri closed the door, it is forbidden, for then the Nochri does not fear. This is only when Isur is available, like the case there, that he can be Menasech with his hand. If not, even if he closed the door, it is permitted. The Ran and Rashba say like Tosfos, that we are concerned for switching only if the Nochri would benefit. R. Chananel permits leaving a Nochri in the house with meat on a fire only if the Yisrael locked him in, so he cannot bring Isur from outside, and we know that there is no Isur in the house. The others permit Stam, which implies that even if he did not lock the door and there is Isur in the house. It seems that R. Chananel argues with them.

Shach (32): The Gemara concludes that when a Yisrael goes in and out, l'Chatchilah one may leave a Nochri there. It says 'ha'Meniach', which connotes b'Di'eved, for the case when he delayed a long time. The Rema (129:1) says that then it is b'Di'eved. This is like the Mordechai. Tosfos says that ha'Meniach connotes l'Chatchilah.

Shach (33): Even a minor going in and out helps, like the Rema said (115:1), even for an Isur Torah. The Mechaber (69:10) says so about rinsing salt off meat. Even though cooked blood is not an Isur Torah, it seems that this affects only believing a Nochri who spoke Lefi Tumo (unaware of the consequences). A Nochri fears lest he be seen, for an Isur Torah or Isur mid'Rabanan.

Shach (34): We permit as long as we do not know that he closed the door, like it says in 129:1.

Gra (29): Going in and out helps even for Shechitah, in which any amount of Drisah (pressing the knife into the Siman) disqualifies.

Shulchan Aruch (12): One should be stringent not to leave pots with slaves when there is no Yisrael in the house.

Gra (36): This is when no one goes in and out, e.g. when he goes to the Beis ha'Keneses. It is as if he said that he will be away for a while. Sometimes slaves put in milk to get a better portion. We permit when a Nochri heard people calling that it is time to pray, for he knows that the Yisrael suspects him; it is permitted because the Nochri will not profit. (Perhaps this refers to nowadays, that he has no lust to be Menasech - PF.)

Bedek ha'Bayis: The Rashba (1:761) says that if a Nochri would need to lose to cause a Yisrael to transgress, we are not concerned. However, perhaps this is only b'Di'eved, but l'Chatchilah one may not rely on this. A support for this is that in a city in which Yisre'elim slaughter and most of the meat is Kosher, meat found with a Nochri is permitted (Chulin 95a), yet l'Chatchilah one may not send meat with a Nochri without a seal. There are many neighborhoods of Yisre'elim in which the b'Di'eved Heter applies, but no where do people send l'Chatchilah with Nochri without a seal.

Rema: This is if he does not go in and out.

Shach (34): In a Teshuvah the Rosh permitted when a Shomer going in and out. This is letter of the law, but l'Chatchilah one should not rely on this, like he said in his Pesakim! The Rema infers that since he did not advse the questioner to be stringent, he holds that it is l'Chatchilah in this case. One should be stringent when going to the Beis ha'Keneses, for the slave knows that he delays there.

Rema: If the slave put Isur in the pot, we do not give to her to eat from it, lest he accustom her do to so.

Shach (38): This is from Shibolei ha'Leket. Shibolei ha'Leket said that she put in the Isur to anger her master. He only excludes when she did not know that what she put in is Isur. Surely we are concerned lest she do so again if she intended for her benefit!

Shach (39): Shibolei ha'Leket forbids giving to any Nochri. Surely the Rema agrees; 'to her' does not exclude other Nochrim.

Pischei Teshuvah (7): Tiferes l'Moshe says that if she put in Isur to anger her master, we do not give to any Nochri. If she intended for her benefit, we may give to other Nochrim, for she did not fulfill her intent.