Question: Which takes precedence, what is more Tadir, or what is more Kodesh?

Yevamos 39a (Mishnah): The Mitzvah is for the oldest brother to do Yibum. Even if he wants to wait for the oldest brother to return from overseas, we tell him to do Chalitzah or Yibum now.

This is because we do not delay the Mitzvah.

47b (Beraisa): If he still wants to convert (after hearing about some Mitzvos), we circumcise him immediately.

This is because we do not delay a Mitzvah.

Yoma 6b (Rav Nachman): Tum'as Mes is permitted b'Tzibur.

(Rav Sheshes): It is Dechuyah (pushed aside) b'Tzibur.

Version #1: If there are Tamei and Tahor Kohanim in the Beis Av (those who are scheduled to serve today), all agree that only the Tehorim serve. They argue (in a case when there are not Tehorim in the Beis Av) about whether we seek Tehorim from a different Beis Av. (Rav Sheshes says that we do.)

Version #2: They argue even when there are Tehorim in the Beis Av. (Rav Nachman permits the Temei'im to serve.)

33a (Reish Lakish): We do not pass over Mitzvos.

Rashi (Yoma 33a DH Ein): The Mechilta teaches that Ein Ma'avirin Al ha'Mitzvah, for then it is delayed and sours.

Terumas ha'Deshen (35): If one sees the moon on a weekday, if soon will be Motza'ei Shabbos and it is not too far into the month, e.g. it is the seventh or eighth, it is good to wait until Motza'ei Shabbos. Even if it will be cloudy, and also two or three or four days afterwards, he still has time to bless until the 15th of the month. Or Zaru'a says that we bless on the moon only on Motza'ei Shabbos when we are sweet smelling and wearing nice clothing. However, if Motza'ei Shabbos will be late in the month, and if it will be cloudy that night and two or three or four days afterwards, the time to bless will pass, one should not wait for Motza'ei Shabbos. Whenever there is a reasonable chance that a Mitzvah will be lost, we do not delay it, even in order to do it ideally. We learn from Yevamos 39a. This is only if there is a reasonable chance lest the Mitzvah be lost. We do not wait for a minor to mature, or for an older brother to return from overseas, lest the minor die or the older brother never return, and the Mitzvah will pass. (Note: if the minor dies, the remaining brother(s) could do Yibum or Chalitzah. Seemingly, the concern is lest she die, and the Mitzvah will be lost!) It does not say that we do not wait for him to return from another part of Eretz Yisrael, for we are not concerned. Hagahos Maimoniyos says that when Maharam would bless during the week, so the time would not pass, i.e. the 16th, he would wear his honorable jacket. This does not mean that the time would surely pass before Motza'ei Shabbos, rather, that there was a Safek that it would pass.

Shulchan Aruch (OC 426:2): We say Kidush Levanah only on Motza'ei Shabbos when one is wearing nice clothing.

Rema: If Motza'ei Shabbos will be after the 10th of the month, we do not wait, lest there be three or four cloudy days and he will lose the Mitzvah.

Kaf ha'Chayim (23): If the time for Kidush Levanah came, one should not delay in order to be Mekadesh amidst many people, for Zerizin Makdimim l'Mitzvos overrides "b'Rav Am" (Kitzur Shulchan Aruch 97:9).

Rema (OC 625): It is a Mitzvah to build the Sukah immediately after Yom Kipur. One should not sour an opportunity to do a Mitzvah.

Magen Avraham (1): He should build the entire Sukah (immediately).

Birkei Yosef (2): Eliyahu Zuta holds that one should not make the Sukah before Yom Kipur, based on the Yalkut (Emor 653). However, I saw meticulous people make the walls and Sechach before Yom Kipur, and on Motza'ei Yom Kipur they place the Sechach. If not all of it, they put at least some of it.

Moreh b'Etzba (of the Birkei Yosef, 285): One should strive to make something of the Sukah on Motza'ei Yom Kipur, to fulfill "... v'Yakov Nasa Sukosah." A Chacham will prepare beforehand something he can begin immediately on Motza'ei Yom Kipur. This does not contradict what he says here that one makes the walls before Yom Kipur, for only the Sechach is called Sukah. There is no Mitzvah to make the walls. It is only Hechsher Mitzvah. If they are already made, e.g. walls of the house, they are Kosher for Sukah. However, Moreh b'Etzba connotes that he may do anything for the Sukah, even not of the Sechach. Perhaps this is because it is hard to build (so quickly) from the foundation (to what will hold the Sechach).

Sha'arei Teshuvah (1): Eliyahu Rabah makes a mere Asmachta that one should not begin before Yom Kipur. Dwelling in the Sukah alludes to exile. The Sukah itself does not! If so, it would be good to build it earlier, so it can help tip the scales of judgment, like the Levush says about Kidush Levanah!

Mishnah Berurah (2): In the previous Siman, the Rema discussed the night of Motza'ei Yom Kipur, and taught that it is a Mitzvah to make a mere start. The next day, one should fix all of it, if possible. Also, at night is for meticulous people. Even if one is not meticulous, he should start the next day after returning from the Beis ha'Keneses and finish it if possible. This is even if it is Erev Shabbos, but then one may not work on it after midday.

Shevus Yakov (1:34): If one has a Kosher Esrog at the time of Hallel, but an hour or two later he will get a better one, he should wait for it.

Yad Eliyahu (42): In Siman 37, Shevus Yakov says that if one prepared wax candles to light, and they brought olive oil to him, he should light the candles he prepared, for it is as if he already started the Mitzvah. I disagree. As long as he did not bless and light, it is as if he did not start. If an Ones occurred and he did not light, surely they are not Asur b'Hana'ah! It is difficult to say that he holds like the opinion that they are forbidden through Hazmanah (designation). We hold that designation does not forbid!

Sha'arei Teshuvah (651:8/17): I say that Zerizim Makdimim l'Mitzvos (he should not wait for a better than Esrog). The Magen Avraham (25:2) learns from Yevamos 39 that we do not delay Mitzvos (to do them better later). We say so about Kidush Levanah. In Yevamos, we say that when a prospective convert accepts to convert, we circumcise him immediately. Beis Yakov (142) says that the entire day is called immediately. This is like R. Shimshon and the Bartenura in Taharos (9:4). See CM 190:16 (if a seller was anxious for the money, paying him that day is considered paying immediately). Tzemach Tzedek 104/120 says that one who swears to pay immediately has the entire day. After this is called delaying. The custom regarding Bris Milah is to be zealous and circumcise in the morning. However, if one knows that he will do the ideal Mitzvah, one may wait even a long time, as long as he is sure that he will do the ideal Mitzvah. Also this is called zealous. Yoma 6b proved this. (According to the opinion that Tum'ah is Dechuyah b'Tzibur, we seek Kohanim Tehorim for the Avodah. If there are no Tahor Kohanim who are supposed to serve today, we seek Tehorim who are not supposed to work today.)

Rema (684:3): If on Rosh Chodesh Teves one mistakenly began to read the Kri'ah for Chanukah, he must interrupt and read the Kri'ah for Rosh Chodesh.

Magen Avraham (5): Even though Ein Ma'avirin Al Mitzvos, here the order is Me'akev. This is like one who pulled the head Tefilin out of the bag before the hand Tefilin.

Rebuttal (Taz 4): The Avudraham says that since we learned that they are Me'akev, this implies that if one put them (Tefilin) on out of order, he was not Yotzei and he must put them on in order. It seems that he holds that similarly, if one read the Kri'ah for Chanukah before that of Rosh Chodesh, he must go back and read them in the proper order. This is astounding! There is no such Gemara about Tefilin. The Beis Yosef brings two opinions about one who removed the Shel Rosh from the bag before the Shel Yad, but he connotes that all agree that if he put on the Shel Rosh first, he need not remove it! There is no reason to do so. If one needed to do so, this is a bigger Chidush, and the Shulchan Aruch should have taught it. We expounded that 'when they are between your eyes, there should be two' (you should be wearing also the Shel Yad). Since now he wears both, he fulfills this! The same applies to reading the Kri'ah for Chanukah first. Even though he transgressed and did not do the more regular Mitzvah first. This is clear from Zevachim 90b, which asked whether we offer first the more regular or more Kodesh Korban. If one who transgressed 'Tadir Kodem' was not Yotzei even b'Di'eved, surely one must do the more regular first! Another proof is from Zevachim 12a, in which we say that Tefilas Minchah precedes Musaf, for it is more regular, and it compares this to other cases of Tadir. We hold that one who prayed Musaf first was Yotzei (OC 286:4)! This is unlike one who prayed Tashlumim before the current Tefilah. He was not Yotzei, for one must pray the current Tefilah first. There, it was not time for Tashlumim. He is like one who prayed not in the time of Tefilah. One may not rely on this ruling of the Rema. Also, there are two opinions about whether one must bless again on what was already read. Why should one make a Safek Berachah?!

Rebuttal (Korban Nesan'el Megilah 4:3 (29b)): The Rema holds that Tadir (Rosh Chodesh occurs more frequently than Chanukah) overrides not passing over Mitzvos. This is wrong. Tosfos (Yoma 33a) asks why a verse needs to teach about putting Shirayim of inner Chata'os on the western Yesod; we already know this because we do not pass over Mitzvos, even though the southern Yesod is Tadir (most Shirayim are poured there).

Bi'ur Halachah (DH v'Im): Many Acharonim argue with the Rema. If they mistakenly opened the Torah prepared for Chanukah, if the Olah already said Hash-m's name in Birkas ha'Torah they should read Parashas Chanukah. If not, they should close the Torah and begin with the Torah prepared for Rosh Chodesh. Even the Magen Avraham here merely explains the Rema, but it is clear from what he wrote in Siman 140 that he holds like the Taz.

Kaf ha'Chayim (26): Eliyahu Rabah says that if he already read three verses in Parshas Chanukah, he finishes, and the next three read the Kri'ah for Rosh Chodesh. If he did not yet read three verses in Parshas Chanukah, he interrupts and reads the Kri'ah for Rosh Chodesh, and the fourth reads for Chanukah. However, the other Acharonim hold like the Taz.