The Hazara of Musaf of Rosh Hashana is a very important Tefila, since the Shofar is blown after each of the three main Berachot: Malchuyot, Zichronot and Shofarot. According to some authorities, these Shofar blasts are the primary fulfillment of the Misva. Therefore, it is incumbent upon everyone to pay close attention the repetition of Musaf. If one is distracted by talking or even learning (which is also prohibited), it is considered as though he did not hear these Shofar blasts in their properly ordained place, following the sequence of the Berachot. Rather, one should follow the repetition with a Siddur, along with the Hazzan.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) in Parashat Teruma strongly emphasizes the obligation to give proper respect to the Hazara, adding that it is even more important than the silent Amida. Nobody would dream of talking during the silent Amida, how much more so one must be careful in the Hazara.
Of course, the importance of answering Baruch Hu U’Baruch Shemo and Amen cannot be underestimated. The Pele Yoetz (Rabbi Eliezer Papo, 1785–1828, Bulgaria) describes the harsh punishment that awaits those who neglect to respond Baruch Hu U’Varuch Shemo and Amen, saying that their fate is in the lowest level of Gehinnom. Conversely, If people would realize the sublime reward that awaits those who answer a Beracha, they would run after every possible opportunity to do so, as though it was a great treasure.
One is obligated to pay careful attention to the Hazara of Musaf of Rosh Hashana.