Continuity mistake: In the scene right after Shelly's funeral when Kate and 'Adam' are talking by his car, he goes to kiss her when they are done. He tries to kiss her on the lips, but she moves to the side. At first he is kissing her on the left cheek and when the camera changes positions, he is kissing her on her right cheek. (00:17:50)
Continuity mistake: When Adam gives Kate the lollipop as a gift, Kate writes "IOU TLC" on a laundry ticket. As she takes the ticket out her bag, there is the number "6443" printed in red on it. When she hands him the ticket though, the number is now "6335." (00:47:55)
Continuity mistake: When Campbell is in the basement, he drops a book of matches. They fall all over the floor, but in the next shot they change their position and lay in a neat little formation. (00:55:30)
Answer: Plot hole? Or perhaps Adam's / Jeremy's nose was bleeding because he was about to snap Kate's neck. Or it was because he was so happy.
Alan Keddie
He killed Dorothy at the end that could be why his nose bleeds.