I don't know anything about the actual "Staircase" case. My wife offered to tell me, and I said I'll wait until after the show; the only information I did get was the parents at the center of the story—Colin Firth and Toni Collette—adopted orphaned neighbor kids, which doesn't seem to matter yet. This episode quickly introduces the family—two parents, five kids, no pets—in an Ordinary People-esque montage where we find out son Dane DeHaan has a troubled history they don't talk about, and daughter Olivia DeJonge is jealous of at least one of her (presumably adoptive) siblings.
The episode—and presumably the series—uses a fractured narrative device to reveal various things about the case and the family, including how 9/11 will figure into the story. While the episode starts with old man makeup Firth putting on a tie nearer the present (2017), the main action occurs in fall 2001. Firth and Collette are sending youngest daughter Odessa Young off to college (here's where DeJonge's jealous), then later—after multiple flash aheads—Collette hurts herself at their empty nesters' party. Instead of being worried about her at the hospital, Firth mansplains 9/11 to her.
Because it's based on a true story, "The Staircase" is about whether Firth killed Collette one night in December 2001 or if she really did just get drunk and fall down a treacherous staircase in their Durham, North Carolina home. Shockingly good Patrick Schwarzenegger gets home from a Christmas party to find the cops all over and Firth freaking out. Schwarzenegger immediately believes Firth's story, though the cops are already talking about how Collette'd been long dead before Firth's 911 call (hence the episode title), where he says she's still alive.
The episode will then be Firth acting exceptionally mysterious and guilty, even before the episode reveals he's having an affair, even before we find out he lied in a mayoral campaign about getting a Purple Heart in Vietnam. There's the additional problem Firth's playing a Southern white guy and is immediately believable as a wife-killer. Hell, his lawyer brother Tim Guinee seems like he could've killed his wife, ditto district attorney with a vendetta (writer Firth is nasty to the cops in his newspaper column) Cullen Moss, ditto Firth's own defense attorney Michael Stuhlbarg, who's a Yankee transplant.
But Firth's excellent. Collette's really good too, but she doesn't get anywhere near as much, which is why I was really hoping she wouldn't be the victim. Instead, it's all about Firth straddling awkward and murderous.
The supporting cast is all good, with Parker Posey coming in at the end to knock it out of the park as a member of the D.A.'s team. Guinee's rote but okay; he's mostly just there for exposition dumps about how it's got to be a witch-hunt and to introduce Stuhlbarg to the plot.
The direction from Antonio Campos is fine. The draw's the large cast, who seem like they'll all eventually get more to do as the series progresses.