How could the people see that Aharon had died?
Rashi #1 (citing the Tanchuma and the Sifri): When Moshe descended without Aharon and told the people that Aharon had died, they could not believe that the Angel of Death could overcome the man who had stood up to him and stopped the plague, until, in answer to Moshe's Tefilos, the Mal'achei ha'Shareis showed them Aharon lying on a bed.
Rashi #2 (citing Rosh Hashanah, 3a): The Pasuk is not saying that the people saw that Aharon had died but that they were seen 1 because Aharon had died. 2
Targum Yonasan: They saw that the Clouds of Glory had disappeared 3 and that Moshe descended the mountain with rent clothes and weeping over the death of Aharon his brother, 4 at which point , they too wept over his death for thirty days.
See Ba'al ha'Turim.
Because the moment Aharon died, the Ananei Kavod that accompanied them on the merit of Aharon and which hid the people from view from the outside, departed.
See Ba?al ha?Turim.
Targum Yonasan: Lamenting 'Woe is me that you have died, Aharon my brother, the pillar of the Tefilos of Yisrael'.
Why does the Torah write here "Vayivku ? Kol Beis Yisrael" and when Moshe died, ?Vayivku ? B'nei Yisrael? - Devarim 34:8?
Rashi and Targum Yonasan: Because when Aharon died, both the men and the women mourned his death because he pursued Shalom, bringing together disputants, and husbands and wives who had fallen out. 1 Whereas when Moshe died, only the men wept - Rashi, Devarim 34:8.
Hadar Zekenim: Once a man became angry with his wife, expelled her from his house and swore that she would not return until she spat in the Kohen Gadol's face. Aharon heard, and told her that he had an eye ailment, and the only cure would be for her to spit in it. Afterwards he sent her to her house; she told her husband, and [so Aharon] made Shalom between them.