This is probably the best of the random plots from the first season. Still, the same idea was done better by Voyager in "Worst Case Scenario."
Basically, "Dramatis Personae" artificially creates a situation where all the main characters are pushed into their most extreme behaviors, forcing the underlying tensions the series has built at least a part of its premise around to rise to the surface. In Voyager, that meant finally seeing a dramatic confrontation between the Starfleet and Maquis members of the crew via a holodeck program booby-trapped by the one Maquis who actually did exploit what some fans always assumed was inevitable (Seska). Here, it's pretty much the same, with tensions between Starfleet and Bajoran personnel bubbling to crisis.
Now, some of this might seem a little strange to fans who aren't too familiar with the early development of Deep Space Nine. They might be surprised to learn how hostile Kira was to Starfleet's presence. Outside of this episode, it was really only apparent in the pilot; otherwise, other than the difference in uniform she became such a loyal collaborator with Starfleet that she might as well have been a member. This is not a criticism of the series, but rather a way to explain what exactly this episode is supposed to accomplish.
In short, "Dramatis Personae" was almost an anachronism from its original airdate. In a way, this is exactly the kind of episode that would have driven fans crazy in a different Star Trek, or pointed out things they wished had been happening all along. Heck, this one may actually be the reason Deep Space Nine was the first of the franchise black sheep.
Anyway, a couple things worth pointing out. Odo is at the center of this story, being the typical individual unaffected by the weird things going on (which could also make this a fine episode to watch if you like that kind of Star Trek adventure), though I have no particularly strong memories of this being significant to the character one way or another. Also, one of the quirks Sisko develops leads him to building an intricate clock, which can still be seen in his office well past this episode, and it foreshadows his ability and interest, even while not under the influence, to build a Bajoran solar ship in "Explorers" two seasons later. So there are a couple of ways to view this episode as more significant than it really is, but I don't want to exaggerate its worth.
Have a look at it and judge for yourself.
franchise * series * essential * character
Memory Alpha summary.