Revealing mistake: When Nelson first undergoes the experiment, the doctors use a small mask to put him to sleep. When he is supposedly waking up, Rachel asks Randy to help her with oxygen. He hands her the same small mask they used the first time ie. anesthetic. Just for a second she has a look on her face which says "this is the wrong mask" and she tries to hide it with her hand. For the whole rest of the film, the other doctors use a bigger mask when giving oxygen.
Revealing mistake: Rachel's father's suicide: After he heads down the stairs (during her death experiment), we suddenly hear a popping sound like a gunshot, as the girl follows her mother outside, to see glass littering the pavement. Then the camera flipping to shots of an old pickup parked on the curbside. And a single bloodied gunshot hole through the windshield. Which would not have happened within the 5-second time, between the stairs and the curb.
Answer: Billy forgave Nelson. he saw that Nelson was willing to die to be forgiven. That's why Billy smiled.
MasterOfAll