The Enterprise is pulled into mediating an agreement involving the Acamarians and their renegade subculture of "Gatherers" (a better word would be "pirates"), who broke off from mainstream Acamarian society a century ago and now live as criminal exiles. Acamarian leader Marouk (Nancy Parsons) reluctantly agrees to try to bring the Gatherers back into her society now that Acamarian life has given up its warlike ways.
Picard attempts to get everyone to sit down together at the negotiation table, but it won't be easy. The Gatherers open fire at the first sight of anyone that comes near their camp. The leader of this particular clan of Gatherers is Brull (Joey Aresco), who agrees to the negotiations. But there's also a murderer going around killing very specific Gatherer individuals, taking revenge (we eventually learn) in a long-ago blood feud. The killer, unbeknownst to everyone but us, is Yuta (Lisa Wilcox), who is Marouk's personal servant and also a young woman that Riker attempts to romance.
"The Vengeance Factor" is a borderline incoherent mess, with a plot that — okay, it does hold together, but it's a really rough road to get there. There are too many characters and not enough investment in any of them. There is no clear line of drama, making it very difficult to become involved in the story. We get dull negotiation scenes, then lackluster romantic scenes, then halfhearted character scenes. The story initially makes much of Brull, an obnoxious vulgarian who is at first menacing and then kind of likable, and then he becomes irrelevant to the story and disappears. The "romantic" scenes between Riker and Yuta are awkward and ineffective. They serve only to set up the final act, in which Riker is tragically forced to kill Yuta to stop her from carrying out the story's titular vengeance factor. The story's message is acceptable. Its execution is not.