Gemara

104b (Agra, father-in-law of R. Aba - Beraisa): Fowl and cheese may be eaten wantonly.

(Agra): This means that one need not wash his hands or clean his mouth in between.

105a (Mar Ukva): I am (sour) like vinegar in comparison to my (virtuous) father, who was like wine. He would not eat cheese for 24 hours after eating meat, but I eat cheese at the next meal!

(Rav Idi bar Avin): Washing before the meal is a Mitzvah. Washing after the meal is an obligation.

Question (Beraisa): Washing before and after the meal is an obligation. Washing (between courses) during the meal is Reshus (optional.)

Answer: Washing before the meal is really a Mitzvah. The Tana calls it an obligation in comparison to Reshus.

136b (Rav Nachman bar Yitzchak): Nowadays, people conduct according to the lenient opinions of R. Ila'i regarding Reishis ha'Gez, and of R. Yoshiyah regarding Kil'ayim;

(Beraisa - R. Ila'i): Reishis ha'Gez applies only in Eretz Yisrael.

(R. Yoshiyah): One is liable for Kil'ai ha'Kerem only if he seeds two diverse species and a grape seed together.

Shabbos 23a (Rav Sheshes): Ner Chanukah is obligatory upon someone lodging outside his house.

(R. Zeira): When I was single and learning from my Rebbi, I would contribute a Perutah towards the cost of the Neros.

Rishonim

Rosh (11:3): Rav Nachman bar Yitzchak taught that nowadays people follow R. Ila'i regarding Reishis ha'Gez. I explained that the same applies to Matanos. Even so, Rabanan explained the Halachos at length, because Rav Nachman did not explicitly say that this is the Halachah, just that it is the custom. In a place where it is not the custom, people must know the Halachos!

Mordechai (736): Rashi was asked why people do not give Matanos nowadays. The Mishnah says that it applies even after the Churban. The latter Amora'im gave them. Rashi answered 'we do not protest against one who gives. He will be blessed! However, the custom is like R. Ila'a, and the same applies to Matanos. Whenever it says 'the custom is', not only we do not expound in the Shi'ur, rather, even we do not rule (unlike the custom). If one did (give), we do not return them. Rabbeinu Meir says that even though R. Ila'i exempts even regarding Matanos, regarding Matanos the custom is unlike him.

Yam Shel Shlomo (11:11): Seemingly, one should know the Halachos in every place, so if one wants to be stringent and give, he will know how to fulfill the Mitzvah! It seems that the Rosh argues with Rashi, who says that one who gives will be blessed. Rav Nachman taught about Reishis ha'Gez together with Kil'ayim, which is a Halachah, not just a custom. Therefore, one who obligates himself in what Chachamim exempted is a Hedyot. However, I wrote that regarding Matanos it is proper to be stringent.

Mordechai (687): Someone asked Maharam why his custom is not to eat beef after cheese, but he eats fowl. He answered 'in my youth I used to deride people who do so. It seemed like Minus (heresy), until once at a meat meal I found cheese between my teeth. I decreed on myself to be stringent about meat after cheese just like for cheese after meat. This is not arguing with the Gemara, nor adding to it; one who does so detracts. Mar Ukva said that he is like vinegar compared to his father's stringency. Everyone may be stringent for himself. I am lenient about fowl, for the Gemara says that they may be eaten wantonly.

Terumas ha'Deshen (101): A Gadol ruled that a guest may light Ner Chanukah without a Berachah. Even though the Gemara said 'now that I married, surely I need not light', this means that he is not obligated. If he wants, he may light. It is not a Berachah l'Vatalah. He is one of the Mehadrin (everyone in the household lights, to glorify the Mitzvah). Also, perhaps they will forget to light in his house. The Gadol said that once he relied on his wife, and she did not light because she assumed that he will light where he is. One of his Talmidim, also a Gadol, said that since he is exempt, if he lights, he is called a Hedyot. All the more so it is a Berachah l'Vatalah, since we do not find this Hidur in the Gemara. I say that the concern lest his wife forget is not enough to override the rules of the Gemara, that one may rely on his household, even for an Isur Kares. If one returns home and finds his wife sleeping, if he calculates that based on her normal menstrual period she was able to become Tahor, she is permitted. We are not concerned lest she erred or forgot. Also here, if she or the household or her neighbors know that the Mitzvah is incumbent on whoever is in the house, one relies on them. Even if once an error occurred, we are not concerned it happen again. This is like it says in Avodah Zarah (33b), that one may put beer in a Nochri's barrel. Even though a certain Amora once put in wine, we are not concerned lest this happen again. Maharam connotes that it is not considered adding to the Gemara only because Amora'im were stringent. If not, it would be called adding, even though he once stumbled. He would not be stringent due to this. All the more so, one should not say a Safek Berachah l'Vatalah. However, perhaps just like there is a Hidur for everyone in the house to light, perhaps it is a Hidur for both a man and his wife to light in two places. The Tana did not teach this, for it is not common. Since the Gemara discusses Mehadrin and Mehadrin Min ha'Mehadrin, this is not adding to the Gemara.

Yam Shel Shlomo (Chulin 8:5 DH Gam): R. Tam says that even though washing during the meal is Reshus, it is somewhat of a Mitzvah. Therefore, l'Chatchilah one should conduct (stringency) like the Rashbam. Whenever the Gemara mentions 'Reshus', if one wants to be stringent, it is permitted and proper. It is not considered haughtiness, like we say that it is haughtiness to wash the hands for Peros, or if one is exempt and fulfills, he is called a Hedyot. This is even regarding a Mitzvah, like Semag says. Here one may be stringent. Even R. Tam admits, just he does not call it an absolute obligation. In any case only regarding washing the custom is to be stringent, because food sticks to the hands, and when he eats the latter food, the foods will mix. We are not stringent about cleaning and rinsing the mouth, due to mixing of tastes or due to food between the teeth, since it is not intact. The custom is that during the day, we are more lenient about washing after cheese than about cleaning and rinsing. Since one can see (if anything remains on his hands) we leave the law like according to the Gemara (washing is Reshus). Whenever one must wash, he must also clean and rinse. Regarding Reshus, there is no place for a stringency to clean and rinse between courses.

Yam Shel Shlomo (6): Even if one is careful about all separations, he may not be stringent to refrain from eating meat after cheese, unless he once stumbled, or he has cavities and almost surely he cannot clean his teeth. In any case one may command his household not to bring to him meat after cheese in the same meal. After the Gemara was sealed we should not be stringent unlike the Gemara, unless one stumbled, and also Chachamim of the Gemara were stringent for themselves about this. If it is not brought to the table, it does not look like Minus (being more stringent than the Gemara).

Yam Shel Shlomo: Maharam said that initially, it looked like Minus in his eyes. This implies that if one did not stumble, he may not be stringent. Since the primary Heter to be stringent is that he once stumbled, why did he mention that Amora'im were stringent? Terumas ha'Deshen says that a mistake that occurred once is not a reason to be stringent, if not that we find that Amora'im were stringent. Surely it is not the case that every Amora who was stringent once stumbled! If so, why did Mar Ukva call himself 'vinegar, the son of wine'? (This question assumes that Mar Ukva did not stumble - PF.) Rather, Amora'im could add stringencies. However, after the Gemara was sealed, we may not add stringencies if not that one stumbled once, and Amora'im were stringent.

Poskim

Shulchan Aruch (YD 89:2): If one ate cheese, he may eat meat immediately afterwards, as long as he checks his hands that none of the cheese stuck to them. If it is night and he cannot check them well, he must wash them. He must clean his mouth and rinse it. This is to eat meat of a Behemah or Chayah afterwards. If he will eat poultry after cheese, he need not clean or wash.

Rema: Some are stringent even for meat after cheese. This is the custom. If the cheese is hard, we do not eat after it even poultry, just like we do not eat cheese after meat. Some are lenient. One should not protest, just they should clean and wash the hands. However, it is good to be stringent.

Taz (4): However, after old cheese that is not wormy, that was not made from milk curdled in a stomach, rather, from regular milk that was dried, or after butter, it suffices to clean (the mouth) and remove particles from the teeth and rinse the mouth and hands, unless one wants to be extra stringent.

Shach (17): The Yam Shel Shlomo said that it is like Minus to be stringent. Only Maharam was stringent, for once he stumbled. Really, Maharam connotes oppositely!

Gra (11): The Zohar is stringent. We do not say that it is against the Gemara, for also they (Chachamim of the Gemara) used to be stringent.

Sifsei Da'as (20): The Pri Chodosh says that one who eats with a fork need not wash in between cheese and meat. It is proper to be stringent about a matter if it is not a burden.