Stephen Dorff and Elle Fanning spent a lot of time together prior to the shoot in order to build the father-daughter relationship their characters have. For example, Dorff sometimes picked Fanning up after school.
A number of the dialogs were improvised by the actors, notably the things said by Sammy (Chris Pontius) to Cleo (Elle Fanning). This was done in order to provoke genuine surprise from Fanning. Pontius, in fact, was specifically chosen for his improvisation skills, as well as his good rapport with children.
The film's "Golden Lion" win at the Venice Film Festival was highly controversial, with some people questioning President of the Jury Quentin Tarantino's objectivity due to Sofia Coppola being a former girlfriend of his.
Cleo is talking to Johnny about a vampire book she is reading which sounds a lot like "Twilight". Cleo is played by Elle Fanning whose sister, Dakota Fanning plays Jane in three of the Twilight Saga films.