Responsa על ברכות 52:2

We were also unsure regarding the statement in the Mishnah, "The afternoon prayer may be recited until evening" (Berachot 4:1). Does this refer to sunset, or to the time when the stars become visible? For when reading the words of Rabbi Yehuda carefully, he claimed that the prayer could be recited until 'plag hamincha'¹a point in the day ten and three-quarter hours after sunrise. In the Talmudic discussion (Berachot 26b:15), they ask whether this word 'until' includes the whole last portion of the day, or means up until that point of time. They then argue that if 'until' includes the last portion of the day until the twelfth halachic hour, then Rabbi Yehuda would not be in disagreement with the other rabbis [which he seems to be]. Therefore, it seems that when the rabbis say 'until evening', they also mean until the twelfth hour, which is the time that the stars are visible in the sky² according to the understanding of the Talmud in Berachot 2b:4. Regarding all this I asked [in my dream] whether, in the case of a headache³meaning of Hebrew unclear or in other extenuating circumstances, one could recite the afternoon prayer until the time the stars are visible?⁴The Talmud finishes its discussion of the correct time for the afternoon prayer inconclusively (Berakhot 27a:14), yet the question here assumes a normative practice of finishing it early, before 'plag mincha', and is asking about extenuating circumstances. R. Hai Gaon quotes the contemporary practice in the Babylonian academies to recite the afternoon prayer up to nightfall when necessary (Shibbolei Haleket 47). The 12th-century provençal work Sefer Hashlama writes that people were not consistent, and sometimes said the afternoon prayer late or the evening prayer early (cited in Beit Yosef Orach Chaim 233). The contradiction between these two practices is discussed in Tosafot on Berakhot 2a:1.

R. Jacob, the cantor of Magdeburg, died and left a son, Hizkiyahu, who was worthy to succeed his father as cantor of Magdeburg, though inferior to him in some qualities. A majority of the membership of the Magdeburg community wanted the son to succeed his father, but a minority of possibly one or more strongly objected to the son. R. Moses b. Hisdai was asked for his opinion in the matter. He advised Hizkiyahu to try any measure in his power to ingratiate himself with the objectors. He asked the leaders of the community to direct their efforts toward effecting a reconciliation with the opposing faction, and expressed his opinion that a single person could not defy the will of the entire community. R. Isaac b. Moses (of Vienna) stated that according to Biblical Law a community could not hire a cantor to whom there was objection even by a single person. R. Meir stated his opinion that a cantor might officiate throughout the year even though not acceptable to a few congregants, but that he was not permitted to officiate on Rosh Hashanah and Yom Kippur or on fast days, if even a single congregant found him objectionable.
SOURCES: L. 109–11; Or Zarua I, 21a.