1. Reviewing the prayers:
The Chazan for Rosh Hashanah and Yom Kippur should review the Davening, the meaning of its words, and the Midrashic and Chassidic teachings on the prayers. This especially applies to the Piyutim in Davening. This is to be done every year even if he did so the previous year. He is also to review the laws of prayer in general and especially those that specifically pertain to the Chazan. Every individual is to review the prayers and teach it to his children prior to the Holiday.
The Piyutim: Whoever has the ability is to take out time to learn the meaning of the Piyutim recited during the prayer.
2. Correct punctuation and Nussach:
During the ten days of repentance, which begin from Rosh Hashanah, one must be extra careful in punctuating the words of Davening correctly. Due to this a number of laws regarding punctuation and dialect of wording is recorded in Poskim.
3. Saying Shir Hamaalos in Shacharis:
It is customary to recite the psalm of Shir Hamaalos Mimamakim between Yishtabach and Barchu throughout the ten days of repentance. [It is not the Chabad custom to open the ark when the psalm is recited, and we do not repeat each verse after the Chazan. However in some communities the above customs are followed. The above psalm is to be recited even when praying in private.]
If the Chazan forgot to recite Shir Hamalos and already began Kaddish, what is to be done?
If the Chazan already began Kaddish then he is to finish the Kaddish and continue straight with Yotzer Or. The psalm of Shir Hamaalos is to be omitted.
If one is holding in middle of Pesukei Dezimra may he say Shir Hamaalos together with the congregation?
Yes. Furthermore, upon reaching Yishtabach he may repeat Shir Hamaalos, prior to Yotzer Or.
If a certain community was accustomed not to recite Shir Hamalos between Yishtabach and Yotzer, may they change their custom?
If majority of the congregation desires to take upon themselves this custom, and they have the consent of the community, then they may do so.
Sparks of Kabala & Chassidus
The depths of the soul:
Proper Teshuvah: Teshuvah is the expression of the inner depths of the soul. When one does Teshuvah from the most inner part of his heart, this then arouses above a revelation from the most inner aspect of G-dliness. In order to correct spiritual blemishes caused through sin one must tap into the original source, drawing from the “supernal depth.” This is analogous to a river that has become dry: when it is filled from a flowing well-spring, it returns to its former state. This is the meaning of the scriptural verse “from the depths I call to you”: the elicitation is from the “supernal depth.” We draw from this “depth” by calling to G-d from the depth of the innermost soul. This is possible not through speech, but only through crying out. In the continuation “G-d hear my voice,” the phrasing is not literally “my voice,” but rather “in my voice”. This means that G-d should listen and accept what is “in the voice,” its internal aspect, the innermost heart.
Two levels of depths: The first depth refers to the cry of the heart which is from the level of Chaya of the soul. This is referred to in “Bechol Libi Derashticha”. However the level of Mimamakim [plural tense] refers to the depth of this depth which is the cry of the Yechida, the essence of the soul.
Building the Sefira of Malchus: This scream from the inner soul, the essence of the soul, reveals G-d’s essential desire to be king over His people, and assists in the building of the Sefira of Malchus.
The ten depths:
There are ten levels of depth recorded in Sefer Yetzira. Each day of Aseres Yimei Teshuvah one of these levels of depth is revealed. The word “Omek” [depth] and Gevura share the same Gematria [numerical value] which is 216. This is because each of the ten depths refers to a different level of Gevura. The ten levels correspond to the ten Sefiros, each level corresponding to a Sefira. Thus the purpose of reciting this psalm during Aseres Yimei Teshuvah is to sweeten the Gevuros. Each day one is to intend to sweeten the specific Gevura of that day.
 Beir Heiytiv 581/7 “Learn the prayers and supplications”; Igros Kodesh 6/324; 11/353 and 416 [brought in Shaarei Halacha Uminhag 1/247; Shulchan Menachem 3/93]; See Mateh Efraim 581/48; 585/2; Darkei Chaim Veshalom 702; M”A 581/9 in name of Shlah “Learn the Kavanos”
 Igros Kodesh ibid; Shaareiy Teshuvah 584/3
 Rebbe ibid
 Igros Kodesh 11/353
 Kaf Hachaim 582/26; Mateh Efraim 581/58
 Shaareiy Teshuvah 584/3; Kaf Hachaim 584/13
 The reason: Since these are days of judgment [the words one says, even if his intent is otherwise, have affect, thus] one is to place special care in pronouncing the words with their correct punctuation. However during the rest of the year we do not suspect for a mispronunciation as [G-d] follows the person’s intention behind the word. [ibid]
 List of words and their correct punctuation, and correct Nussach: Lechaim versus Lachaim [Admur 582/7]; Lechaim Tovim versus Lechaim [582/8]; Mentioning Rosh Chodesh; Yom Teruah versus Zichron Teruah [582/9]; Omitting Moadim Lesimcha; Omitting Vehasieinu; Omitting Ein Anu Yecholim in Musaf [582/10] Udvarcha Emes versus Udvarcha Malkeinu by both Haftorah and Kiddush [582/11; Siddur-Udvarcha Malekinu Emes; Shaar Hakolel 42/11; Poskim in Kaf Hachaim 582/55] Shehashultan with Kamatz versus Shehashilton with Chirik [582/12; Levush; Taz 582/2; Mateh Moshe; Peri Chadash brought in Kaf Hachaim 582/37] Veharisha with Chirik under Shin. [582/13] Vechein Tzaddikim versus Az Tzaddikim [582/14] Yom Teruah Mikra Kodesh and Zichron Teruah Mikra Kodesh versus Beahava Mikra Kodesh. [582/14; Poskim in Kaf Hachaim 582/41] Uvichein Yiskadesh Shimcha-four times Uvichein based on Kabala. [Kaf Hachaim 582/35] Hayom Haras Olam-according to Kabala. [Kaf Hachaim 582/36] Aguda Echas versus Eguda Echas with a Patach or Segol [Mahril; Kneses Hagedola; Peri Chadash; Kaf Hachaim 582/37] Vesikva Tovah Ledorshecha versus Vesikva Tovah [Kaf Hachaim ibid in name of Arizal] Kol Harisha versus Ki Kol Harisha [Mateh Moshe 796; Kaf Hachaim ibid] Beashan Tichleh versus Keashan Tichleh [Mahril; Mateh Moshe; Peri Chadash; Siddur Rashash; Siddur Admur [Beashan]; Shaar Hakolel 42/6; Likkutei Mahrich 63a; M”E 692/14; Darkei Chaim Veshalom 711; Kaf Hachaim 582/37] Saying Beyom Menuchaseinu on Rosh Hashanah that falls on Shabbos [Poskim brought in Kaf Hachaim 582/48] Meloch Al Kol Haolam Kulo versus Meloch Al Haolam Kulo [Poskim brought in Kaf Hachaim 582/50]
Lechaim versus Lachaim Tovim: First one is to mention Lechaim and only afterwards in Ukesov Lechaim should he say Lechaim Tovim as first one asks for a small requests and then increases in asking for more. [582/8]
 Siddur; Shaar Hakavanos 90; Peri Eitz Chaim Shaar Rosh Hashanah 7 [brought in M”A 54/2 in name of Kesavim]; Degul Merivava 54; M”B 54/4; Mateh Efraim 584/9; 619/37; Ketzei Hamateh 584/17; Beir Heiytiv 603/1; Pesach Dvir 54/2; Minchas Ahron 12/28; Chesed Lealafim 54/1; Kaf Hachaim 54/8; 582/14; Aruch Hashulchan 54/2; Toras Chaim Sofer 54/2; Likkutei Mahrich Seder Rosh Hashanah; Igros Moshe 2/21
Background of the custom: This custom is based on the writings of the Arizal [Peri Eitz Chaim, brought in Shaar Hakolel 6/15]. The custom is mentioned by the Magen Avraham 54/2, although he himself concludes with a question as to whether reciting this psalm during prayer constitutes an interval. Admur in his Shulchan Aruch chapter 54 completely omits this topic even though it was mentioned in the M”A ibid, and Admur in general records the rulings of the M”A. However in the Siddur of Admur the psalm was inserted. The M”B 54/4 writes the exact wording of the M”A and also concludes with the same question regarding an interval. The Degul Merivava 54 answers the question of the M”A ibid by stating that the prohibition of an interval is only applicable regarding matters irrelevant to prayer and not with regards to words of praise. So also answer the Aruch Hashulchan 54/2; Toras Chaim Sofer 54/2 against the question of the M”A. The Kaf Hachaim [54/8] brings Poskim which rule that it is to be said without deterrent, and he plainly rules so in 582/14, and so is the custom.
Other customs: Some communities are not accustomed to recite Shir Hamalos at all during Aseres Yimei Teshuvah. [See Igros Moshe 2/21] See Kaf Hachaim 54/8 in name of Nachalas Ariel that one who does not know the Kavanos of this Mizmor is not to recite it. In conclusion the Kaf Hachaim negates this ruling.
Hoshana Raba: Some communities are accustomed to recite Shir Hamaalos also on Hoshana Raba. [See Piskeiy Teshuvos 54 footnote 24 for a list of communities and Tzaddikim who follow this custom] Some argue vehemently against the allowance to do so being that such a custom has no source in the writings of the Arizal and hence is considered an interval. [Siddur Tzelusa Deavraham] It is not the Chabad custom to recite it on Hoshanah Raba.
Custom to recite Hashem Hu Haelokim: Some have the custom to recite “Hashem Hu Haelokim” twice prior to reciting Hashem Melech before Baruch Sheamar. [Siddur Rashash; Siddur Beis Oved] The reason for this is because these days are an atonement for the sin of the golden calf, and it is thus befitting to recite the verse as did Eliyahu Hanavi. [Avodas Hatamid brought in Kaf Hachaim 582/13] Nevertheless in the Siddur Arizal this is not mentioned, and it is likewise not mentioned in the Poskim. [Kaf Hachaim ibid] Practically this custom is omitted from the Siddur of Admur.
 All Poskim ibid; The Ketzei Hamateh ibid states that the entire Segula of this psalm is when it is said specifically between Yishtabach and Yotzer Or.
Other opinions: Some are accustomed to recite the psalm after Shemoneh Esrei prior to Tachanun. However according to all the Poskim above, and the words of the Ketzei Hamateh, it is certainly to only be recited between Yishtabach and Yotzer, especially being one is not allowed to delay Tachanun after Shemoneh Esrei. [Iyunei Halachos 1/1]
 Otzer Minhagei Chabad Rosh Hashanah 184
 Darkei Chaim Veshalom 709 [regarding repeating verse by verse with the congregation]
 See Mateh Efraim 619/32; Ahalecha Beamasecha 37/24; This is unlike the opinion of Teshuvos Vehanhagos 2/41 that says it is not recited when praying without a Minyan.
 Ketzei Hamateh 582/17; Toras Chaim Sofer 54/2 [that one may not make an interval between Kaddish and Yotzer]; Piskeiy Teshuvos 54/4 [however see there footnote 29 that the Klozinberger Rebbe had this occure to him one time and he recited the Shir Hamaalos and then repeated the Kaddish]
 Regarding what is considered the start of Kaddish-see Ashel Avraham Butchach 55; Piskeiy Teshuvos 55/8 that even if one began the first word it is considered that he began Kaddish with regards to concluding it if there is no longer a Minyan. Vetzaruch Iyun regarding this matter.
 Mateh Efraim 619/32; Alef Lamateh 584/2; Vetzaruch Iyun as even to say it between Yishtabach and Yotzer the Poskim are in question, hence how can we allow it to be said in an area that it was never instituted or accustomed to be done even initially. Perhaps however since the custom is accepted based on the ruling that words of praise may be recited during Pesukei Dezimra, therefore here too it is allowed.
 Alef Lamateh 584/2; As the entire affect of this Mizmor is specifically when it is said between Yishtabach and Yotzer [Ketzei Hamateh 584/17]
 Igros Moshe 2/21
 Likkutei Torah, Rosh Hashanah 54c
 Mamar Besukos Teishvu 1963
 Mamar Besukos Teishvu 1963
 Shaar Hakavanos 190; Peri Eitz Chaim Shaar Rosh Hashanah 7; Kaf Hachaim 582/14; Darkei Chaim Veshalom 709
 The first Omek/Gevura which is revealed on the first day is Gevura of Keser. The second Omek/Gevura which is revealed on the second day is Gevura of Chochmah. The third Omek/Gevura which is revealed on the third day is Gevura of Bina. The fourth Omek/Gevura which is revealed on the fourth day is Gevura of Daas. The fifth Omek/Gevura which is revealed on the fifth day is Gevura of Chesed. The sixth Omek/Gevura which is revealed on the sixth day is Gevura of Gevura. The seventh Omek/Gevura which is revealed on the seventh day is Gevura of Tiferes. The eighth Omek/Gevura which is revealed on the eighth day is Gevura of Netzach and Hod. The ninth Omek/Gevura which is revealed on the ninth day is Gevura of Yesod. The tenth Omek/Gevura which is revealed on the tenth day is Gevura of Malchus. [Peri Eitz Chaim ibid in name of Rameh]