I loved the third season, but it did bounce back and forth between episodes on Millennium Group world domination/annihilation, purely religious stories, and serial killer themes.
Your reference to the 'weird serial murderer of the week' syndrome recalls an episode involving two guys with special forces training, who would randomly murder strangers, a case which reminded Emma of the murder of her sister many years earlier, by a man who eerily resembled (but was not) one of the two killers. I tried to track down that episode, but couldn't.
I thought the sexual chemistry between Lance Henriksen (Frank Black) and Klea Scott (Agent Emma Hollis) was torrid, even if -- or because? -- it was never consummated. I am convinced that Chris Carter had planned on Frank and Emma having an affair in the fourth season.
Because the show was cancelled, and Carter had only an episode or two left, he had to make some hard decisions, and couldn't resolve all the prominent story lines. Although the "Frank and Emma" story line was very important, it was secondary to the "Frank and Peter Watts" thread, which ran through the length of the series, and was its moral heart. Carter had set up a brother-type relationship -- both men had the same green eyes, and even the same, athletic gait -- in which Peter appeared to be "Cain" to Frank's "Abel." But that wasn't the case. Peter WAS his brother's keeper, and died to save Frank. That was arguably the dramatically most important thing the final episode did; otherwise, the entire series would have lost much of its narrative and moral coherence.