First-Person (Libby Day); Third-Person Limited (Ben and Patty Day)
Dark Places gives us three different P.O.V. characters (okay, technically four—but more on that in a minute), each character with his or her own dark places to explore.
The character who ties everything together is Libby. Her story serves as a frame of sorts, and as a result, it's told in first person. Although it's told in the past tense, you figure out clues as Libby does within these sections. It's a mystery, and you're along for the ride.
However, as a reader, you get more information than Libby ever could. Flynn accomplishes this by giving us third-person accounts of what happened on the fateful day of January 2, 1985. Ben and Patty get their own sections, alternating with Libby's, in a pattern of Libby, Patty, Libby, Ben, Libby, Patty, and so on. Libby as a seven-year-old sometimes shows up as a character in these sections, which is illuminating, because Libby has unclear memories of her childhood.
Libby isn't a purposely unreliable narrator. She may be a thief, but we think she's honest with us. However, the crime happened long, long ago, and afterwards, Libby was coached to give false testimony. She has no idea what's real and what isn't. Her brother Ben isn't talking from jail, so we need his sections to explain what really happened on that night.
Of course, Flynn is writing a suspense story, so she's not going to lay out all her cards on page one. The third-person sections are carefully structured to hide details from us. Diondra's pregnancy and Patty's arrangement with a hit man are major details that are known to (some of) the characters but are hidden from us until a moment for maximum surprise arises.
Speaking of the hired hit man who kills Patty, Calvin Diehl strangely gets his own chapter, chapter 40 (out of 43 total). This reveals his dark place as well. As a hit man, he's felt perfectly justified killing everyone he killed… except young Debby. He'd never killed a child before, or anyone who hadn't asked for it. Diehl is distraught over this. This is something Libby will never learn. Does it change the way you think of him?