129:2 Some have the practice to recite all the Shemoneh Esrei prayers of Rosh Hashana and Yom Kippur bowing and bending their heads. We must bow at the beginning and the end of the brachos “Magen Avraham” (“shield of Abraham”) and “Modim” (“we give thanks”), so those who pray bowed must straighten up when they reach these brachos so that they can bow in the appropriate places. We are not permitted to bow at the beginning or end of any bracha other than the ones specified by the Sages (therefore, he would have to straighten up for the start and end of each bracha – Mishnah Brurah 582:14). It would be better for one to pray with his limbs straight, with a humble heart and tears. One who is accustomed to pray aloud on Rosh Hashana should not do so; he should pray quietly as we do the rest of the year. Some authorities permit one to raise his voice a little louder than usual but not much. One should carefully enunciate his prayers so that he doesn’t change any vowels. One should pray from a reliable siddur or machzor.
129:3 The rest of the year in Shemoneh Esrei, we say “ha(k)Eil hakadosh” (“the holy G-d”) and “Melech oheiv tzedaka u’mishpat” (“the King Who loves righteousness and judgment”) but from Rosh Hashana through Yom Kippur, one must say “haMelech hakadosh” (“the holy King”) and “haMelech hamishpat” (“the King of judgment”). This is because G-d judges the world in this period. If one accidentally said “ha(k)Eil hakadosh,” or if he was unsure whether he said “ha(k)Eil hakadosh” or “haMelech hakadosh,” then if he realized immediately, he says “haMelech hakadosh” and he does not need to go back to the beginning of Shemoneh Esrei. This is also the case for “haMelech hamishpat.” If one did not realize quickly enough, then he must return to the beginning for “haMelech hakadosh,” even in a case of doubt. (If he started the next bracha, it’s too late even immediately after – MB 582:7.) This is because the first three brachos are considered a single unit. Even the shaliach tzibbur must go back to the beginning during the repetition of the Shemoneh Esrei, even though this means saying Kedusha a second time. However, when it comes to “haMelech hamishpat,” even an individual does not go back, not even to the start of the same bracha. This is because the regular text of the bracha also acknowledges G-d as King. (If one said “Melech hamishpat” rather than “haMelech hamishpat,” it is acceptable after the fact – MB 118:2.) If one accidentally said “haMelech hakadosh” or “haMelech hamishpat” during the rest of the year, he does not go back.