The Shulchan Aruch (Orah Haim 142:1) explains that if one makes a mistake, even involving only one letter, while reading the Torah, he must repeat the word correctly. The Rama (ibid.) modifies this approach by saying that the reader need be corrected only if his mistake changed the meaning or context of the word. Furthermore, the Rama states that a mistake in the cantillation (“Te’amim”) or in punctuation (“Nikud”) is not grounds for correcting the one reading the Torah, however, he should be reprimanded. According to Rabbi Avraham Buchach (Eshel Avraham), the the Rama’s intention of “reprimanded” means that the reader should be told in a gentle manner of his mistakes after the Torah reading so that he may correct them in the future. Certainly, publicly reprimanding the reader in a harsh tone is forbidden. Although not grounds for correcting the reader at the time of the Torah reading, the Zohar gives tremendous importance to the proper singing of the cantillation, and the Bet Yosef explains that even on a practical level, they are useful in setting the rhythm and pauses in each verse.
Rabbi Shlomo Zalman Auerbach (Halichot Shlomo, ch.18 § 24) gives practical guidelines as to what does and does not require a reader to be corrected at the time of the Torah reading: a) Confounding Mil’el and Milra’ (placing emphasis on the penultimate, versus the final syllable of a word, respectively); b) repeating a word; c) Confounding Shva Na and Shva Nach (when the Shva is pronounced like an “e” vowel, versus not being pronounced at all, respectively) are example of errors which need not be corrected. On the other hand, mistakes in emphatic cantillation notes such as Shalshelet, or even Sof Pasuk, which have contextual significance, should be corrected at the time of the reading.
Interestingly, the Brisker Rav (Shu”t Teshuvot VeHanhagot, vol. 5 § 37) was particular that one should hear the Torah being read according to one’s tradition. Nevertheless, the overwhelming consensus is that one fulfills one’s obligation to hear the Torah in any rite, be it Ashkenazic, Sephardic, etc.
Summary: Certain errors, which do not change the meaning or ontext of a word or verse, do not need to be corrected when the Torah is being read.