Corrected entry: Lisbeth drops her keys while visiting Miriam in hospital; Mikael, who Miriam gives them to, says they are from a Post Office Box, and that's how he finds out where Lisbeth lives, by emptying her Post Office Box. But those keys don't have the location of the Post Office or the number of the box attached to the key; that's why people use them - for privacy and safety.
Corrected entry: While Lisbeth is being buried alive, you can see a hole in the dirt near her face, so the actress playing her can breathe. The hole isn't completely covered over; the camera pans away.
Correction: Mikael is the kind of guy who really would go from post office to post office, box to box, until he found the one the key unlocked. He is an investigative journalist, that's the kind of thing he does all the time to get to the bottom of a mystery.
Phixius ★