Everybody's speaking about some revelation in the finale, but what I saw is Durst denying writing the letter and then proceeding to restroom. We hear the sound of his pants dropping and him mumbling for next five minutes. I think he also says "Killed them all of course" in ironic manner being annoyed by constant accusations.
I'm not saying he didn't killed them, he probably did, but I'm not sure what the sensation was.
The last scene where he was presented with the envelope evidence basically set up the scene in the bathroom where he didn't realize (again) that his microphone was still on.
In the envelope scene we see him denying he wrote both when there is almost a zero chance that is true.
In the end scene he basically is talking himself through what just happened. Have you ever been in a situation where you know you 'stuck your foot in it' and pretty much want to kick yourself for it? He seems to be in that state of mind at the end, and the things he says, while some are a little incoherent are basically an admission of guilt. "What a disaster ..."; "he was right, I was wrong"; "I'm having difficulty with the question"; "what the hell did I do?"; and finally, "killed them all, of course."