Our practice is that when we read from the sefer Torah, both on Shabbos and on weekdays, we read the pessukim with a special tune, commonly referred to as the "trup". Rav Soloveitchik zt"l said in the name of his grandfather R' Chaim that his practice would be to correct the ba'al koreh even if he only made a mistake in the "trup". The Gemara in Nedarim presents a disagreement amongst the Amoraim whether the requirement to read the Torah with a special tune is biblical in nature or only rabbinical.
This coming Shabbos is commonly referred to as "Shabbos Shira". Oz Yoshir is read with a tune which is different than the regular trup; the tune used is a cheerful one, and sounds like a victory march. Why don't we utilize the usual trup when we read Oz Yoshir?
In many shuls, the practice is that in addition to Oz Yoshir (which begins in perek 15) being sung in this unique way, an additional possuk (in perek 14) is also sung with this special marching tune. That possuk describes how when the waters of Yam Suf split and there was a dry path through it, the water was piled up to the right and to the left like tall walls. This description appears twice, once in 14:22 and a second time in 14:29. My impression is that the common practice is for the baal koreh to only read the second possuk, which appears almost immediately before Oz Yoshir, with the special marching tune. Rav Soloveitchik zt"l said that from where he came from in Europe, the practice was the opposite, and only the first possuk (14:22) was recited with the cheerful nigun.
The reason for distinguishing between the two pessukim, despite their being nearly identical, is that the spelling of one of the words is different: in 14:29 the word "choma" is spelled without the letter vov, (i.e. it is spelled choser) while in 14:22 it is spelled with a vov (i.e. moleh). The Midrash comments that the reason for the change is to allude to the fact that at the time of Yetzias Mitzrayim, despite all of the nissim and niflaos, osos u'mofsim, and gilui Shechina that everyone had witnessed, there was a character by the name of Michah who brought an idol with him from Egypt. Later, in Sefer Shoftim, the story is told of Michah getting many Jewish people to worship this idol. The word "choma - wall", when spelled without a vov, can be read "cheima - anger". Hashem was angry that despite of all of the osos u'mofsim etc., Michah was taking an Egyptian avoda zara along with him. It would not make sense to use a cheerful tune when reading a possuk which is implying that Hashem was angry. That is why the custom in Eastern Europe where Rav Soloveitchik zt"l came from was that only when reading 14:22 does the baal koreh employ the cheerful, march-like tune to sing about the walls of water to the right and to the left of Bnai Yisroel. Rav Soloveitchik zt"l was very mapkid on observing minhagim, but only with precision and accuracy.
Because so many talmidei chachomim were killed by the Nazis, many minhagim or details of minhagim were lost. Rabbi Soroya Devilitzsky of Bnei Brak, who was a member of the inner circle of the Chazon Ish, published a luach many years ago where he quotes Rabbi Soloveitchik zt"l saying that the haftorah for parshas Kedoshim which is printed in all Chumashim was never recited in certain parts of Lithuania. In the days of the Tanoim, the person who got maftir had the right to select any section of navi to be read as the haftorah, provided that it had a connection to the sedrah. The mishna quotes R' Eliezer saying that it is highly improper to choose the nevuah of Yechezkel haNavi where he was instructed by Hakodosh Baruch Hu to complain to the Jews of Yerushalayim about many of them violating laws of arayos. Despite the fact that R' Eliezer's opinion is outvoted by the majority of the other Tanoim, the minhag developed over the years that we never recite the haftorah of Kedoshim. When we read Acharei Mos and Kedoshim together, we only read the haftorah of Acharei Mos. And, when the two sedrahs are read separately, the Shabbos of parshas Kedoshim is either Rosh Chodesh or erev Rosh Chodesh and the haftorah is therefore either "Hashomayim kisi" or "Mochor chodesh". When the two sedrahs are read separately and the Shabbos of parshas Kedoshim is neither Rosh Chodesh nor erev Rosh Chodesh, the minhag in Lithuania was that they still would not read the haftorah for Kedoshim from Yechezkel. They would read the haftorah for Acharei Mos two weeks in a row. Again, Rav Soloveitchik zt"l was very mapkid on keeping minhagim, and transmitted the details of the minhagim with accuracy and precision.