Is one required to unroll his Megila before the Megila reading on Purim, or should he keep it rolled and open it as the reading progresses?
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes that one should open the Megila scroll in its entirety before the reading, specifically, before the Berachot recited over the reading (listen to audio recording for precise citation). However, Hacham Ovadia Yosef explains the Ben Ish Hai’s comments as referring specifically to the Hazan, the one who reads the Megila for the congregation. He should open the entire scroll before the reading, and keep it open with one part folded over the other. The congregants, who listen silently to the reading while following along in their own scrolls, do not unroll their Megilot before the reading. They keep it closed and open it as the reading progresses, leaving it open until the conclusion of the reading. After the reading, they roll the Megila.
The reason for this custom is the fact that Megilat Ester is referred to as an "Iggeret," which means a "letter" or "document," as opposed to a Torah scroll, which is never described with this term. Letters are usually left wide open as they are read, and it is therefore customary to keep the Megila open (whereas a Torah scroll is kept closed except for the page currently being read). However, as mentioned, the Hazan opens the Megila in its entirety before the reading, whereas the congregants open the scroll as the reading progresses.
Summary: The Hazan who conducts the public reading of the Megila should open the scroll completely before the reading, folding one part of the scroll over the other. The congregants, who follow along with their own Megilot, open their Megilot as the reading progresses, and leave it open until the conclusion of the reading.