Plot hole: According to the phone book the name given was "M. Horowitz" but when Mary mails he first letter to him she already knows it's "Max."
Other mistake: When Max is reading the note Mary left on the first page of her book, the words Mary speaks continue on the next page, but Max never turns the page.
Continuity mistake: When Mary first opens the phone book at the post office she lands on Finklestein but when she puts her finger on the name she chooses it as Hororwitz, even though she never turned the page again.
